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Calculating limits are standard with math functions. It's used to evaluate the maximum value a mathematical function can reach. For example, f(x) denotes a function that is dependent on the variable x. The limit will determine the maximum value of f(x) as x approaches infinity or negative infinity. The mathematical nature of the function will determine the limit. For this reason, to calculate the limit, you simply need to know mathematically evaluate the function given hypothetical values of x.
Instructions
1. Choose an exponential function. As an example, choose f(x) = y^x
2. Calculate the limit of the function as x approaches infinity. Using the example function:
For 0 < y < 1, limit (y^x) = 0. This is because as you increase x to infinity any fraction between 0 and 1 will trend to 0. For example:
If y is .40 and x is 3, f(x) = 0.064. If y is 0.40 and x is 12, f(x) = 0.000017. If y is 0.95 and x is 5, f(x) = 0.77. If y is 0.95 and x is 15, f(x) = 0.46. If y is 0.95 and x is 60, f(x) = 0.046. In each case, f(x) trends toward 0, which means the limit is 0.
For y = 1, limit (y^x) = 1. 1 to any power is 1
For y > 1, limit (y^x) = infinity. As x increases on any number greater than 1, the value of f(x) increases continuously to infinity.
3. Calculate the limit of the function as x approaches negative infinity. Using the example function:
First, we have to adjust the function to account for a negative x or "-x": f(x) = y^-x = (1/y^x)
For 0 < y < 1, limit [(1/y^x)] = infinity. Here's why:
If y = 0.40 and x = 5, f(x) = 1/[0.40^5] = 1/ 0.01024 = 97.65. This number will increase as x increases.
For y > 1, limit [(1/y^x)] = 0. Here's why.
If y = 4 and x = 5, f(x) = 1/(4^5) = 1/1024 = 0.000975. As x increases, the denominator will continue to increase and f(x) will continue to decrease and trend toward zero
Tags: approaches infinity, Calculate limit, Calculate limit function, example function, function approaches