Calculus 1 Exercises

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Master calculus fundamentals through comprehensive problem-solving practice with this extensive video collection covering essential Calculus 1 topics. Work through hundreds of exercises systematically organized to follow the typical sequence of a first-year calculus course, from basic function classification through integration techniques. Tackle limit problems using algebraic manipulation, conjugate rationalization, squeeze theorem, and trigonometric identities, while exploring continuity, discontinuities, and the Intermediate Value Theorem. Practice derivative calculations using first principles, power rule, product rule, quotient rule, and chain rule with functions involving polynomials, trigonometric expressions, exponentials, logarithms, and inverse trigonometric functions. Develop skills in implicit differentiation, logarithmic differentiation, and finding critical points for optimization problems. Master integration techniques including power rule for integrals, u-substitution, and trigonometric integrals, while solving definite integral problems and area calculations. Access detailed solutions to recent AP Calculus AB and BC Free Response Questions to prepare for standardized exams. Each video focuses on specific problem types that complement main course material, providing targeted practice for skill development and exam preparation in differential and integral calculus.

Syllabus

Classifying Essential Functions (Algebraic, Polynomial, Rational, etc. ...) | Calculus 1 Exercises
Evaluate Limits from Graph | Calculus 1 Exercises
Limit of x/(x^2-x) as x approaches 0 | Calculus 1 Exercises
Limit of (x^2+x+6)/(x-2) by Factoring | Calculus 1 Exercises
Limit of (x^2+x-6)/(x+3) as x approaches -3 | Calculus 1 Exercises
Limit of (x^3-1)/(x-1) as x approaches 1 | Calculus 1 Exercises
Limit of x^3+8/x+2 as x goes to -2 (by Factoring) | Calculus 1 Exercises
Limit of (x^2-4)/(x^3-8) as x approaches 2 | Calculus 1 Exercises
Limit of (sqrt(x+1)-1)/x as x goes to 0 | Calculus 1 Exercises
Limit of (sqrt(2+x)-sqrtx)/x as x approaches 0 (Rationalize with Conjugate) | Calculus 1 Exercises
Limit of (x-16)/(sqrt(x)-4) as x goes to 16 (Conjugate) | Calculus 1 Exercises
Limit of (sqrt(x^2+9)-3)/x^2 as x approaches 0 (Using Conjugate) | Calculus 1 Exercises
Finding Limits with Basic Limit Laws | Calculus 1 Exercises
Limit of (1-e^x)/(1+2e^x) as x approaches Infinity | Calculus 1 Exercises
Limit of (1-x)sin(1/(1-x)) as x approaches 1 | Calculus 1 Exercises
Limit of sin(2x)/tanx as x Approaches 0 | Calculus 1 Exercises
Limit of x*tan(1/x) as x approaches Infinity (no L'Hospital's Rule) | Calculus 1 Exercises
Limit of sin(1/x) as x approaches 0 Does Not Exist | Calculus 1 Exercises
Limit of x*sin(1/x) as x approaches Infinity | Calculus 1 Exercises
Limit of sin(x)/x as x goes to Infinity (Squeeze Theorem) | Calculus 1 Exercises
Limit of x^2*sin(1/x) as x Approaches 0 (Squeeze Theorem) | Calculus 1 Exercises
Limit of x^4*cos(2/x) as x Approaches 0 (Squeeze Theorem) | Calculus 1 Exercises
Limit of sin(1/x)*e^cosx as x goes to Infinity (Squeeze Theorem) | Calculus 1 Exercises
Master Trig Limits with sinx/x as x approaches 0 | Calculus 1 Exercises
Trig Limits with sinx/x as x approaches 0 Master Problems | Calculus 1 Exercises
Limit of tanx/x as x approaches 0 | Calculus 1 Exercises
Limit of tan^2x/x as x approaches 0 (without L'Hospital's Rule!) | Calculus 1 Exercises
Limit of sin(2x)/x as x approaches 0 | Calculus 1 Exercises
Limit of sin(3x)/x as x approaches 0 | Calculus 1 Exercises
Limit of sin(kx)/x as x approaches 0 | Calculus 1 Exercises
Limit of sin^2(x)/x as x approaches 0 | Calculus 1 Exercises
Limit of x*sin(1/x) as x approaches 0 | Calculus 1 Exercises
Limit of x*sin(1/x^2) as x approaches 0 (Squeeze Theorem) | Calculus 1 Exercises
Limit of sinx^2/x as x approaches 0 | Calculus 1 Exercises
Limit of sinx/x^(1/3) as x approaches 0 | Calculus 1 Exercises
Limit of sinx/(x+sinx) as x approaches 0 | Calculus 1 Exercises
Limit of 2(1-cosx)/x as x approaches 0 | Calculus 1 Exercises
Limit of (1-cos(x))/x^2 as x approaches 0 | Calculus 1 Exercises
Limit of (1-cos8x)/2x as x approaches 0 | Calculus 1 Exercises
Limit of (x+sinx)/(x+cosx) as x approaches Infinity | Calculus 1 Exercises
Limit of sinxtanx/x as x approaches 0 | Calculus 1 Exercises
Limit of cosxtanx/x as x approaches 0 | Calculus 1 Exercises
Limit of arctanx as x approaches Infinity | Calculus 1 Exercises
Limit of arctan(1/x) as x approaches 0 from the Right | Calculus 1 Exercises
Limit of ln(sinx) as x approaches Pi from the Left | Calculus 1 Exercises
Limits with Greatest Integer Function | Calculus 1 Exercises
Continuity of the Greatest Integer Function | Calculus 1 Exercises
Discontinuities with the Greatest Integer Function | Calculus 1 Exercises
Intermediate Value Theorem to Find Roots | Calculus 1 Exercises
Show e^(-x^2)=x has Solution with Intermediate Value Theorem | Calculus 1 Exercises
Finding Horizontal Asymptotes of a Function Using Limits | Calculus 1 Exercises
Find Horizontal Asymptotes with Conjugates | Calculus 1 Exercises
Horizontal Asymptotes of (x^2-1)/(x^2+1) | Calculus 1 Exercises
Derivative of x^2 by First Principles (limit definition) | Calculus 1 Exercises
Derivative of 1/x by First Principles (limit definition) | Calculus 1 Exercises
Derivative of x+1/x by First Principles (limit definition) | Calculus 1 Exercises
Derivative of 1/x^2 by First Principles (limit definition) | Calculus 1 Exercises
Derivative of sqrt(x) by First Principles (limit definition) | Calculus 1 Exercises
Why tanx isn't Continuous on [0, pi/2] | Calculus 1 Exercises
|x| is Continuous but not Differentiable | Calculus 1 Exercises
The Only Power Rule Derivative Video You'll Ever Need | Calculus 1 Exercises
Power Rule Master Problems | Calculus 1 Exercises
Derivative of 1/x with Power Rule | Calculus 1 Exercises
Second Derivative of 1/x | Calculus 1 Exercises
Derivative of 1/x^2 with Power Rule | Calculus 1 Exercises
Derivative of 1/x^3 | Calculus 1 Exercises
Derivative of sqrt(x) with Power Rule | Calculus 1 Exercises
Derivative of 1/sqrtx with Power Rule | Calculus 1 Exercises
Derivative of sqrt(x)+1/sqrt(x) | Calculus 1 Exercises
Find Equation of Line Tangent to x^(1/4) at (1,1) | Calculus 1 Exercises
Derivative of Cube Root x | Calculus 1 Exercises
Derivative of Cube Root x^2 | Calculus 1 Exercises
Derivatives with Negative Exponents | Calculus 1 Exercises
Derivatives with the Product Rule | Calculus 1 Exercises
Product Rule Master Problems | Calculus 1 Exercises
Derivative of sqrtx*(x-1) | Calculus 1 Exercises
Derivative of sinxcosx with Product Rule | Calculus 1 Exercises
Derivative of cos^2x with Product Rule | Calculus 1 Exercises
Derivative of sinxtanx with Product Rule | Calculus 1 Exercises
Derivative of sinxcosxtanx | Calculus 1 Exercises
Derivative of xsecx with Product Rule | Calculus 1 Exercises
Derivative of sqrt(x)*e^x with Product Rule | Calculus 1 Exercises
Derivative of x^2e^xlnx (Product Rule with 3 Functions) | Calculus 1 Exercises
Derivatives with the Quotient Rule | Calculus 1 Exercises
Quotient Rule Master Problems | Calculus 1 Exercises
Don't Use the Quotient Rule to Differentiate 1/x | Calculus 1 Exercises
Derivative of x/(x-1)^2 | Calculus 1 Exercises
Derivative of 1/sinx (Quotient Rule) | Calculus 1 Exercises
Derivative of 1/cosx (Quotient Rule) | Calculus 1 Exercises
Derivative of sec(x) with Quotient Rule | Calculus I Exercises
Derivative of cotx (Quotient Rule) | Calculus 1 Exercises
Derivative of sinx/x with Quotient Rule | Calculus 1 Exercises
Derivative of sinx/x^2 with Quotient Rule | Calculus 1 Exercises
Derivative of x/(1+cosx) | Calculus 1 Exercises
Derivative of sinx/cosx with Quotient Rule | Calculus 1 Exercises
Derivative of sinx/(1+cosx) with Quotient Rule | Calculus 1 Exercises
Derivative of cotx/(1+cotx) with Quotient Rule | Calculus 1 Exercises
Derivative of e^x/x with Quotient Rule | Calculus 1 Exercises
Derivative of e^x/(1+x) with Quotient Rule | Calculus 1 Exercises
Derivative of e^x/x^2 with Quotient Rule | Calculus 1 Exercises
Derivative of sinx/e^x with Quotient Rule | Calculus 1 Exercises
Derivative of (sinx+cosx)/(sinx-cosx) | Calculus 1 Exercises
Derivatives with sinx and cosx Master Problems | Calculus 1 Exercises
Chain Rule Master Problems | Calculus 1 Exercises
Derivative of sqrt(x+1) | Calculus 1 Exercises
Derivative of 1/sqrt(x+2) | Calculus 1 Exercises
Derivative of sqrt(1-x^2) with Chain Rule | Calculus 1 Exercises
Derivative of sqrt(x^2+1) with Chain Rule | Calculus 1 Exercises
Derivative of sqrt(x+sqrt(x)) with Chain Rule | Calculus 1 Exercises
Derivative of (x + 1/x)^2 with Chain Rule | Calculus 1 Exercises
Chain Rule with Radical Functions | Calculus 1 Exercises
Derivative of sin(2x) with Chain Rule | Calculus 1 Exercises
Derivative of sin(3x) with Chain Rule | Calculus 1 Exercises
Derivative of sin(4x) with Chain Rule | Calculus 1 Exercises
Derivative of sin(ax+b) | Calculus 1 Exercises
Derivative of sin(x^2) with Chain Rule | Calculus 1 Exercises
Derivative of sin^2(x) with Chain Rule! | Calculus 1 Exercises
Derivative of sin(lnx) | Calculus 1 Exercises
Derivative of sqrt(sinx) with Chain Rule | Calculus 1 Exercises
How to Differentiate Any e^x with the Chain Rule | Calculus 1 Exercises
Derivative of e^2x, e^x^2, e^sinx with Chain Rule | Calculus 1 Exercises
Derivative of e^(-x) with Chain Rule | Calculus 1 Exercises
Derivative of 1/e^x with Chain Rule | Calculus 1 Exercises
Derivative of e^2x (Chain Rule) | Calculus 1 Exercises
Derivative of e^3x (Chain Rule) | Calculus 1 Exercises
Derivative of e^4x (Chain Rule) | Calculus 1 Exercises
Derivative of e^(ax) with Chain Rule | Calculus 1 Exercises
Derivative of e^x^2 (Chain Rule) | Calculus 1 Exercises
Derivative of e^x^3 | Calculus 1 Exercises
Derivative of e^sinx with Chain Rule | Calculus 1 Exercises
Derivative of e^cosx with Chain Rule | Calculus 1 Exercises
Derivative of e^tanx (Chain Rule) | Calculus 1 Exercises
Derivative of e^(1/x) with Chain Rule | Calculus 1 Exercises
Derivative of e^sqrt(x) with Chain Rule | Calculus 1 Exercises
Derivative of e^e^x with Chain Rule | Calculus 1 Exercises
Derivative of ln(2x) with Chain Rule | Calculus 1 Exercises
Derivative of ln(3x) with Chain Rule | Calculus 1 Exercises
Derivative of ln(x^2) without Chain Rule (and with) | Calculus 1 Exercises
Derivative of ln(1/x) with Chain Rule | Calculus 1 Exercises
Derivative of ln(lnx) with Chain Rule | Calculus 1 Exercises
Derivative of ln(sinx) with Chain Rule | Calculus 1 Exercises
Derivative of ln(secx) with Chain Rule | Calculus 1 Exercises
Derivative of sqrt(lnx) with Chain Rule | Calculus 1 Exercises
Derivative of ln|x| (a piecewise derivative) | Calculus 1 Exercises
Derivative of sin(x^2), sin^2(x), and sin(2x) with Chain Rule | Calculus 1 Exercises
Derivative of sin(x^3), sin^3(x), and sin(3x) with Chain Rule | Calculus 1 Exercises
Derivative of sin^2(x), sin^2(2x), and sin^2(x^2) with Chain Rule | Calculus 1 Exercises
Derivative of cos(2x) with Chain Rule | Calculus 1 Exercises
Derivative of cos(ax+b) | Calculus 1 Exercises
Derivative of cos(x^2) with Chain Rule | Calculus 1 Exercises
Derivative of cos^2x with Chain Rule | Calculus 1 Exercises
Derivative of cos(x^2), cos^2(x), and cos(2x) with Chain Rule | Calculus 1 Exercises
Derivative of cos^2(3x) | Calculus 1 Exercises
Derivative of tan(x^2), tan^2(x), and tan(2x) with Chain Rule | Calculus 1 Exercises
Derivative of tan(x^2) with Chain Rule | Calculus 1 Exercises
Derivative of tan^2(x) | Calculus 1 Exercises
Derivative of tan^3(x) | Calculus 1 Exercises
Derivative of sec(x) with Chain Rule (Secant Derivative) | Calculus 1 Exercises
Derivative of sec(x/2) | Calculus 1 Exercises
Derivative of sec^2(x) with Chain Rule | Calculus 1 Exercises
Derivative of sec^3x (Chain Rule) | Calculus 1 Exercises
Derivative of arctan(1/x) | Calculus 1 Exercises
Second Derivative of sqrt(sinx) | Calculus 1 Exercises
Second Derivative of sqrt(cosx) | Calculus 1 Exercises
Limit of x*lnx as x approaches 0 (L'Hospital's Rule) | Calculus 1 Exercises
Derivative of csc(x^2), csc^2(x), and csc(2x) with Chain Rule | Calculus 1 Exercises
Limits with the Natural Log | Calculus 1 Exercises
Limit of lnx/(x-1) as x approaches 1 (L'Hospital's Rule) | Calculus 1 Exercises
Limit of lnx/(x-1) as x approaches Infinity (L'Hospital's Rule) | Calculus 1 Exercises
Limit of lnx/sqrtx as x approaches Infinity (L'Hospital's Rule) | Calculus 1 Exercises
Limit of lnx/x as x approaches 0 from Right | Calculus 1 Exercises
Limit of (e^x-1)/x as x approaches 0 (L'Hospital's Rule) | Calculus 1 Exercises
Limit of lnx/x as x goes to Infinity (L'Hospital's Rule) | Calculus 1 Exercises
Limit of ln(lnx)/x as x approaches Infinity (L'Hospital's Rule) | Calculus 1 Exercises
L'Hospital's Rule Twice! Limit of e^x / x^2 as x approaches Infinity | Calculus I Exercises
Limit of (e^x-1-x)/x^2 with L'Hospital's Rule Twice! | Calculus 1 Exercises
Limit of x^3*e^(-x^2) as x approaches Infinity with L'Hospital's Rule | Calculus 1 Exercises
Limit of e^x/x^n as x goes to Infinity | Calculus 1 Exercises
Limit of x^x as x approaches 0 | Calculus 1 Exercises
How to Solve 1^Infinity Indeterminate Form Limits | Calculus 1 Exercises
Limit of (1+x)^(1/x) as x goes to 0 (L'Hospital's Rule) | Calculus 1 Exercises
Derivative of arcsin(x) with Implicit Differentiation | Calculus 1 Exercises
Derivative of arcsin(x^2), arcsin^2(x), and arcsin(2x) with Chain Rule | Calculus 1 Exercises
How to Find Derivatives of arcsin with Chain Rule | Calculus 1 Exercises
Derivative of arccos(x) with Implicit Differentiation | Calculus 1 Exercises
Derivative of arccos(x^2), arccos^2(x), and arccos(2x) with Chain Rule | Calculus 1 Exercises
Derivative of arctanx | Calculus 1 Exercises
How to take Derivatives of Absolute Value Functions | Calculus 1 Exercises
Derivative of e^xy (Implicit Differentiation) | Calculus 1 Exercises
Derivatives of log Functions with Any Base (and Chain Rule) | Calculus 1 Exercises
Implicit Differentiation with Exponential Functions | Calculus 1 Exercises
Second Derivative Implicitly | Calculus 1 Exercises
2024 AP Calculus AB FRQ 5 Solution | Calculus 1 Exercises
Derivative of x^(1/x) with Logarithmic Differentiation | Calculus 1 Exercises
Derivative of x^x using Logarithmic Differentiation | Calculus 1 Exercises
Find Derivative of x^sqrt(x) without Logarithmic Differentiation | Calculus 1 Exercises
Derivative of (1+x)^x with Logarithmic Differentiation | Calculus 1 Exercises
Derivative of x^e^x (Logarithmic Differentiation) | Calculus 1 Exercises
Derivative of sin(x)^x (Logarithmic Differentiation) | Calculus 1 Exercises
Derivative of 2^x | Calculus 1 Exercises
Linearization of a Function at a Point is Easy! | Calculus 1 Exercises
How to Find Critical Numbers of Functions | Calculus 1 Exercises
How to Find Critical Points with Derivatives | Calculus 1 Exercises
Verify the Conditions of Rolle's Theorem and Find c | Calculus 1 Exercises
Using Rolle's Theorem to Prove Cubic has Exactly One Root | Calculus 1 Exercises
Verify Function Satisfies the Mean Value Theorem | Calculus 1 Exercises
Finding Critical Numbers of Trig Functions | Calculus 1 Exercise
Finding Critical Points of Trig Functions Master Problems | Calculus 1 Exercises
AP Calc Extreme Value Problem (Local Maximum) | Calculus 1 Exercises
Can you Show e^π is Greater than π^e? Use Calculus!
Minimize Area of a Rectangle (Optimization Problem) | Calculus 1 Exercises
Minimize Distance from Point to Parabola (Optimization) | Calculus 1 Exercises
Minimize Distance Between Point and Parabola (Optimization) | Calculus 1 Exercises
Maximize Area Given Perimeter (Optimization) | Calculus 1 Exercises
Maximize Volume of an Open Top Box (Optimization) | Calculus 1 Exercises
The Only Power Rule Integral Video You'll Ever Need | Calculus 1 Exercises
Power Rule Integrals Master Problems | Calculus 1 Exercises
Integral of 1/x^2 | Calculus 1 Exercises
Integral of sqrt(x) | Calculus 1 Exercises
Integral of 1/(1+x^2) with u-Substitution | Calculus 1 Exercises
Integral of 1/x^2, 1/x^3, 1/sqrt(x) with Power Rule | Calculus 1 Exercises
Integral of 1/sqrtx | Calculus 1 Exercises
Integral of 1/(1-x)^2 | Calculus 1 Exercises
Integral of sqrt(1-2x) | Calculus 1 Exercises
Integral of xe^(x^2) with u-Substitution | Calculus 1 Exercises
Integral of e^sqrt(x)/sqrt(x) with u-Substitution | Calculus 1 Exercises
Integral of 1/cos^2x | Calculus 1 Exercises
Integral of sin^2xcotxsecx | Calculus 1 Exercises
Use Pythagorean Identities to Evaluate Basic Integrals | Calculus 1 Exercises
Integral of sin(2x) | Calculus 1 Exercises
Definite Integrals of Absolute Value Functions | Calculus 1 Exercises
More Absolute Value Integrals | Calculus 1 Exercises
Don't Use u-Substitution for These Integrals | Calculus 1 Exercises
Integral of x/(x+1) | Calculus 1 Exercises
Integral of x/(x^2+1) (u-Substitution) | Calculus 1 Exercises
Integral of x^2/(1-x) | Calculus 1 Exercises
Integral of lnx/x with u-sub | Calculus 1 Exercises
Integral of tan(x) with u-substitution | Calculus 1 Exercises
Integral of tan(2x) with u-substitution | Calculus 1 Exercises
Integral of tan^2x with u-substitution | Calculus 1 Exercises
Integral of cot(x) with u-substitution | Calculus 1 Exercises
Integrating Exponential Functions with Substitution | Calculus 1 Exercises
U-Substitution Integrals with Trigonmetric Functions | Calculus 1 Exercises
2024 AP Calculus AB/BC FRQ 4 Solution | Calculus 1 Exercises
Find the Average of tan(x) with Definite Integration | Calculus 1 Exercises
2024 AP Calculus AB/BC FRQ 1 Solution | Calculus 1 Exercises
2024 AP Calculus AB FRQ 2 Solution | Calculus 1 Exercises
2024 AP Calculus AB/BC FRQ 3 Solution | Calculus 1 Exercises
Find Area of Region Bounded by y=sinx, y=cosx, x=0, and x=pi/4 | Calculus 1 Exercises
2024 AP Calculus AB FRQ 6 Solution | Calculus 1 Exercises
Integral of sin^2x | Calculus 1 Exercises
Integral of cos^3x*sinx with u-Sub | Calculus 1 Exercises
Integral of cos^3x | Calculus 1 Exercises
2023 AP Calc AB/BC FRQ Solutions!
2024 AP Calc AB FRQ Solutions!
Math Teacher vs AP Calc AB Exam from 1988! (no calculator, no problem)
Integral of 1/(4+x^2) | Calculus 1 Exercises
Integral of 1/(a^2+x^2) | Calculus 1 Exercises
2024 AP Calculus BC FRQ 2 Solution | Calculus 1 Exercises
2024 AP Calculus BC FRQ 5 Solution | Calculus 1 Exercises
2024 AP Calculus BC FRQ 6 Solution | Calculus 1 Exercises
2024 AP Calc BC FRQ Solutions!
10 Hours of AP Calc AB/BC FRQs (to fall asleep to)