Calculus methods
- How to find the radius of convergence of a power series
Find the radius of convergence of a power series by applying the Ratio Test or Root Test to its general term.
- How to find a Taylor series
A step-by-step guide to finding the Taylor series of a function centered at a specific point by calculating its derivatives and applying the general formula.
- How to find the sum of a geometric series
Calculate the sum of finite or infinite geometric series using standard formulas and the common ratio.
- How to test a series for convergence with the ratio test
Apply the ratio test to determine absolute convergence of infinite series involving factorials and exponentials by evaluating the limit of adjacent terms.
- How to find arc length
Learn how to calculate the arc length of a curve using definite integrals in calculus.
- How to find the volume with the shell method
Learn how to calculate the volume of a solid of revolution using the cylindrical shell method in calculus.
- How to find the volume of a solid of revolution with the disk method
Learn how to calculate the volume of a solid of revolution using the disk method by integrating the area of circular cross-sections.
- How to find the area between two curves
Find the area between two curves by integrating the difference of the upper and lower functions over the bounded interval.
- How to integrate a trigonometric product
Learn how to evaluate integrals of trigonometric products using u-substitution and half-angle identities for sine and cosine.
- How to evaluate an improper integral
Evaluate improper integrals by replacing infinite limits or discontinuities with a variable and taking the limit as the variable approaches the bound.
- How to evaluate a definite integral
Learn how to evaluate a definite integral using the Fundamental Theorem of Calculus by finding an antiderivative and computing the difference at the boundaries.
- How to integrate using partial fractions
A step-by-step guide to evaluating integrals of rational functions using partial fraction decomposition.
- How to integrate by parts
Learn how to evaluate integrals using the integration by parts formula, including setup, steps, and verification.
- How to integrate by u-substitution
Learn how to evaluate integrals using u-substitution by reversing the chain rule.
- How to apply L'Hopital's rule
Learn how to apply L'Hopital's rule to evaluate limits of indeterminate forms like 0/0 and infinity/infinity using derivatives.
- How to solve an optimization problem
Learn how to find the maximum or minimum values of a function using the first and second derivative tests in calculus optimization problems.
- How to solve a related rates problem
Learn how to solve related rates problems in calculus using implicit differentiation and the chain rule to connect the rates of change of multiple variables.
- How to find inflection points
Learn how to find inflection points by identifying where the second derivative of a function changes sign.
- How to find critical points and classify them
A step-by-step guide to finding critical points of a function and classifying them using the first and second derivative tests.
- How to find the equation of a tangent line
Learn how to find the equation of a tangent line to a curve at a given point using derivatives and the point-slope formula.
- How to find the derivative from the limit definition
Compute the derivative of a function using the formal limit definition with exact step-by-step instructions and a fully worked example.
- How to differentiate a function with a variable exponent using logarithmic differentiation
Compute the derivative of functions with variable bases and variable exponents by applying natural logarithms and implicit differentiation.
- How to differentiate implicitly
Learn how to find the derivative of an implicitly defined function by differentiating both sides with respect to x and solving for dy/dx.
- How to differentiate a quotient
Learn how to use the quotient rule to differentiate functions that are the ratio of two differentiable functions.