Limits by Direct substitution

The direct substitution is a basic method in mathematics and it can be used to find the limit of a function in calculus. In this method, the quantity at which the limit should be evaluated is directly substituted in the function to find its limit. So, this method is called evaluating the limits by direct substitution.

Now, let’s learn more about finding the limit of a function by direct substitution.

Cases

There are two different cases, which we should know before using it.

1. If the value of a function is finite after substitution, then the value is called the limit of a function.
2. If in case the value of a function is indeterminate, then the limit of a function cannot be evaluated by direct substitution.

Examples

Now, let’s learn how to find the limit by direct substitution method from some simple limit problems.

Now, let’s see another example to learn the limits by direct substitution method further.

The above two examples express two different cases of finding the limits by direct substitution and they clearly help you to understand how to find the limit of a function by direct substitution method in calculus.

Worksheet

$(1).\,\,$ $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize (x^3-5x+6)}$

$(2).\,\,$ $\displaystyle \large \lim_{x \,\to\, \Large \frac{\pi}{2}}{\normalsize \dfrac{x}{4+\sin{x}}}$

The limit questions on finding the limits by direct substitution method for your practice with solutions to learn how to find the limit by direct substitution in calculus.

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