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One-Sided Limits

"A limit is the value that a function approaches as the input of that function approaches a certain value. In Calculus, sometimes functions behave differently depending on what side of the function th ...

Natural Log Integration

"Because the derivatives of e^x and ln(x) are e^x and 1/x, respectively, the integrals of the latter two functions are just the former. If the variable parts of these functions are not just x, but a p ...

Average Value of a Function

"Calculating the average value of a function over a interval requires using the definite integral. The exact calculation is the definite integral divided by the width of the interval. This calculates ...

Average Rate of Change

"The average rate of change of a population is the total change divided by the time taken for that change to occur. The average rate of change can be calculated with only the times and populations at ...

Maxima and Minima

"Finding relative maxima and minima of a function can be done by looking at a graph of the function. A relative maximum is a point that is higher than the points directly beside it on both sides, and ...

Marginal Cost and Revenue

"The marginal cost and marginal revenue are the additional amount of cost or revenue that arise from producing one more item. If you take the derivative of the cost and revenue functions, you get appr ...

Approximate Area

"When finding the area under a curve for a region, it is often easiest to approximate area using a summation series. This approximation is a summation of areas of rectangles. The rectangles can be eit ...

Antidifferentiation

"Finding the antiderivatives of a function require a little backwards thinking. Since the derivative of the wanted antiderivative is the given function, checking for correctness is easy. You just take ...

Antiderivatives

"Antiderivatives are the opposite of derivatives. An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a functio ...

Logarithm Rule

"The logarithm rule is a special case of the chain rule. It is useful when finding the derivative of the natural logarithm of a function. The logarithm rule states that this derivative is 1 divided by ...

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