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Important Limits

"An important limit in calculus, which is central to finding derivatives of exponential functions, involves finding the limit as h approaches 0 of a special function. This limit, one of a few importan ...

The Fundamental Theorem of Calculus

"The fundamental theorem of Calculus is an important theorem relating antiderivatives and definite integrals in Calculus. The fundamental theorem of Calculus states that if a function f has an antider ...

The Derivative Function

"By definition, the derivative is a function which is derived from another function. The definition of the derivative is usually only written for one point, but the function is defined for all points. ...

The Definite Integral

"The definite integral is an important operation in Calculus, which can be used to find the exact area under a curve. The definite integral takes the estimating of approximate areas of rectangles to i ...

Substitution Method

"The substitution method is a very valuable way to evaluate some indefinite integrals. The substitution method adds a new function into the one being integrated, and substitutes the new function and i ...

General Power Rule

"The general power rule is a special case of the chain rule. It is useful when finding the derivative of a function that is raised to the nth power. The general power rule states that this derivative ...

First Derivative Test

"The first derivative test is a way to find if a critical point of a continuous function is a relative minimum or maximum. Simply, if the first derivative is negative to the left of the critical point ...

Exponential Rule

"The exponential rule is a special case of the chain rule. It is useful when finding the derivative of e raised to the power of a function. The exponential rule states that this derivative is e to the ...

Evaluating Limits Algebraically

"When we evaluate limits that are not continuous, we can use algebra to eliminate the zero from the denominator and then evaluate the limit using substitution. When evaluating limits algebraically we ...

Evaluating Limits

"When we evaluate a limit, we are trying to determine the value that the function is approaching at a certain point. When evaluating limits, we want to first check to see if the function is continuous ...

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