Calculus concepts, explained
- What is the average value of a function?
Learn how to find the average value of a continuous function over an interval using definite integrals, with a clear analogy and worked example.
- How do you find the volume of a solid of revolution?
Learn how to calculate the volume of a solid of revolution using integrals, with everyday analogies and clear steps for the disk and washer methods.
- What is the Fundamental Theorem of Calculus saying?
The Fundamental Theorem of Calculus connects derivatives and integrals, showing they are essentially opposite mathematical operations.
- How do you find the area between two curves?
Learn how to use definite integrals to calculate the area between two curves by subtracting the bottom function from the top function.
- When do you use integration by parts?
Learn when to use integration by parts, how the formula works, and how to choose your parts using the LIATE rule to solve complex calculus problems.
- How do you choose a u-substitution?
Learn how to correctly choose a u-substitution in calculus by looking for functions and their derivatives hiding together inside integrals.
- What does an integral represent?
An integral represents the total accumulation of a quantity, such as the area under a curve, by adding up infinitely many tiny slices.
- How do you find the maximum and minimum of a function on an interval?
Learn how to find the absolute maximum and minimum values of a function on a closed interval using the Extreme Value Theorem and critical points.
- What is a related rates problem and how do you set one up?
A related rates problem uses the known rate of change of one quantity to find the unknown rate of change of another related quantity over time.
- How do you solve an optimization problem step by step?
Learn how to solve calculus optimization problems by finding the objective function, applying constraints, and using the first derivative test.
- How do you find where a function is increasing or decreasing?
Learn how to use the first derivative to find the exact intervals where a calculus function is increasing or decreasing.
- What is Implicit Differentiation For?
Implicit differentiation is a calculus technique used to find the derivative of an equation where y cannot be easily isolated on one side.
- How do you use the product and quotient rules without mixing them up?
Learn how to master the product and quotient rules for derivatives with easy memory tricks and step-by-step examples so you never mix them up again.
- When do you use the chain rule?
You use the chain rule in calculus to find the derivative of a composite function, which happens when one function is nested inside another.
- How do you evaluate a limit that gives 0 over 0?
Learn how to evaluate limits that result in the indeterminate form 0/0 using algebraic techniques like factoring, rationalizing, and L'Hôpital's Rule.
- What does a derivative measure?
A derivative measures the instantaneous rate of change of a function, showing exactly how fast one variable changes relative to another at a specific point.
- What does continuity mean and how do you check it?
Learn the formal calculus definition of continuity, including the three-part limit checklist to prove a function is continuous at a specific point.
- What is a limit in plain language?
A limit in calculus describes the exact value a function approaches as the input gets closer and closer to a specific target.