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Calculus Limit

"In Calculus, a limit is used to describe the value that a function approaches as the input of that function approaches a certain value. There are two ways to determine a Calculus limit: a numerical a ...

Calculating Probability

"Sometimes calculating probability can be fairly complicated, but we have tricks to make it easier. Calculating probability of the complement of an event can be easier than calculating the probability ...

Calculating Equilibrium Concentrations

"The general steps of calculating equilibrium concentrations are to first write out the expression of equilibrium constant, then impute the known concentration value of each element given, and finally ...

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 ...

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