Basic steps for calculating limits of functions:

Consider that f is a real function with 'a' being real number,than limits signifies that f(x) reaches near to L when x reaches near to 'a' i.e. limit of function f of x is L for x -> a. Thus according to the limits calculus, value of f(x) gets close to L as x approaches a. The following are the basic steps tor calculating limits of functions.

  • Put the value of x considering limit as zero.

  • Simplify the numerator and denominator of function.

  • Substitute the values of x and find corresponding value of f(x).

  • The value obtained in above equation gives the limits of f(x).

Calculating limits of exponential functions:

The limits of exponential functions changes significantly with the change in value of x. This is not the case with other functions. If the value of x is a big positive number, the value of f(x) will also be big that can be obtained by calculating limit. It also hold true for low values of x, calculation of limits in such cases provides f(x) with a small value. An example of it will give a clear idea.

(1)Calculate the value of L in calculate limits where a=10 and f(x) = 2x.

Since x approaches 10, value of L = 2x = 2a = 210 = 1024.

What is the left and right hand limit?

The left and right hand limit makes x to approach 'a' from respective side rather than from both sides as done in normal manner.

right hand limitis the formula to calculate limit for f(x) while x approaches 'a' from right.

left hand limitis the formula to calculate limit for f(x) while x approaches 'a' from left.


Method of finding limits from graph:

Consider a graph of f(x) versus x plotted on the x-y plane for finding limits from graph. Now let us plot the valuer of f(x) for the values of x almost near to 'a' for finding out the limit at that point.
finding limits from graph

The figure above shows calculating limit of function f of x at x = 2. The limit of f(x) will be 4 for x = 2.

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