The limit of the simple expression $4x$ has to calculate as $x$ approaches $7$ in this problem and this problem is useful for the beginners. The limit of the function $4x$ can be evaluated by substituting any value that is closer to $7$.

You can take any value that is closer to $7$, for example $x = 6.9917$. There are two reasons for this.

- The value of $6.9917$ is slightly less than $7$ but its approximate value is equal to $7$. In other words, $6.9917 \approx 7$.
- The difference between $7$ and $6.9917$ is also approximately small and negligible. In other words, $7-6.9917 = 0.0083$ and $0.0083 \approx 0$.

The above two points have cleared that the value of $6.9917$ closer to $7$ and substitute it to evaluate the limit of the function as $x$ approaches $7$.

$L \,=\, \displaystyle \large \lim_{x \,\to\, 7}{\normalsize (4x)}$

$\implies$ $L \,=\, 4(6.9917)$

$\implies$ $L \,=\, 4 \times 6.9917$

$\implies$ $L \,=\, 27.9668$

$\,\,\, \therefore \,\,\,\,\,\,$ $L \,\approx\, 28$

Therefore, the limit of the function $4x$ is equal to $28$ as $x$ approaches $7$.

It can also be obtained directly by substituting $x = 7$ in the given function.

$=\,\,\, 4(7)$

$=\,\,\, 4 \times 7$

$=\,\,\, 28$

Therefore, the limit of the function $4x$ as $x$ tends to $7$ is considered as the value of the function $4x$ at $x = 7$ in calculus.

$L \,=\, \displaystyle \large \lim_{x \,\to\, 7}{\normalsize (4x)}$

$\implies$ $L \,=\, 4(7)$

$\implies$ $L \,=\, 4 \times 7$

$\,\,\, \therefore \,\,\,\,\,\,$ $L \,=\, 28$

Theoretically, it is wrong to consider that the limit of the function $4x$ as $x$ approaches $7$ is equal to the value of the function at $x = 7$. However, it is acceptable to consider that they both are equal due to the negligible difference between the input values and also negligible difference between their corresponding values of the function.

Latest Math Topics

Dec 13, 2023

Jul 20, 2023

Jun 26, 2023

Latest Math Problems

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved