Free Calculus Questions and Problems with Solutions
Free calculus tutorials including problems and questions with solutions are presented.
Calculus Problems and Questions
Calculus Questions, Answers and Solutions
Limits and Continuity
Differentiation and Derivatives
- Product Rule of Differentiation with Examples.
- Quotient Rule of Differentiation with Examples.
- Taylor and Maclaurin Series with Examples.
- Find Derivatives of Functions in Calculus using different methods and rules. Several Examples with detailed solutions are presented.
- Difference Quotient. We start with the definition of the difference quotient and then use several examples to calculate it. Detailed solutions to questions are presented.
- Use Definition to Find Derivative. The difference quotient is first calculated then its limitas h approaches zero is computed .
- Proof of Derivative of a^x.
- Derivative of Logarithm function to Any Base : Log_a (x) .
- Proof of Derivative of e^x. The definition of the derivative is used to calculate The derivative of e^x.
- Proof of Derivative of ln(x). The derivative of ln(x) is calculated using the definition.
- Proof of Derivative of sin x. The derivative of sin (x) is calculated using the definition of the derivative as a limit.
- Proof of Derivative of cos x. The derivative of cos (x) is calculated using the definition of the derivative as a limit.
- Derivative of tan(x). The derivative of tan (x) is computed using the quotient rule and the derivatives of sin(x) and cos(x).
- Proof of Derivative of cot(x). The proof of the derivative of cot (x) is presented using the quotient rule and the derivatives of sin(x) and cos(x).
- Proof of Derivative of sec(x). The proof of the derivative of sec (x) is presented.
- Proof of Derivative of csc(x). The proof of the derivative of csc (x) is presented.
- Logarithmic Differentiation. A powerful method to find the derivative of complicated functions. The method uses the chain rule and the properties of logarithms.
- Table of Derivatives. A table of derivatives of exponential and logarithmic functions, trigonometric functions and their inverses, hyperbolic functions and their inverses.
- Rules of Differentiation of Functions in Calculus are presented along with several examples.
- Use of the Chain Rule of Differentiation in Calculus is presented along with several examples.
- Derivatives Involving Absolute Value. Examples on how to find the derivative of functions involving absolute value.
- Implicit Differentiation. Implicit differentiation examples, with detailed solutions, are presented.
- Derivative of Inverse Function. Examples with detailed solutions on how to find the derivative of an inverse function are presented.
- Derivative of Inverse Trigonometric Functions. Formulas of the derivatives of inverse trigonometric functions are presented along with several other examples involving sums, products and quotients of functions.
- Find Derivative of f(x) = arccos(cos(x)) and graph it.
- Find Derivative of f(x) = arcsin(sin(x)) and graph it.
- Find Derivative of f(x) = arctan(tan(x)) and graph it.
- Differentiation of Trigonometric Functions. Formulas of the derivatives of trigonometric functions are presented along with several examples involving products, sums and quotients of trigonometric functions.
- Find Derivative of y = x^x for x > 0.
- Derivative of a Function Raised to the Power of Another Function.
- Differentiation of Exponential Functions is presented. Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined.
- Differentiation of Logarithmic Functions is presented. Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined.
- Differentiation of Hyperbolic Functions is presented. Examples, with detailed solutions, involving products, sums, power and quotients of hyperbolic functions are examined.
Application of Differentiation
Integrals
Integrals of Power of Trigonometric Functions
Differential Equations
Parametric Equations and their Applications
Multivariable Functions (Functions with several variables)
Tables of Mathematical Formulas
- Tables of Mathematical Formulas. Several tables of mathematical formulas including decimal multipliers, series, factorial, permutations, combinations, binomial expansion, trigonometric formulas and tables of derivatives, integrals, Laplace and Fourier transforms.
Interactive Tutorials
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