If $f(5)=7$ and $f^{'}(5)=7$ then $\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}$ is given by
- 35
- -35
- 28
- -28
The Correct Option is D
Solution and Explanation
$=\displaystyle\lim _{x \rightarrow 5} \frac{f(5)-5 f^{'}(x)}{1}$
$=f(5)-5 f^{'}(5) =7-5 \times 7 $
$ =7-5 \times 7 =-28$
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Concepts Used:
Limits And Derivatives
Mathematically, a limit is explained as a value that a function approaches as the input, and it produces some value. Limits are essential in calculus and mathematical analysis and are used to define derivatives, integrals, and continuity.
Limits Formula:
Derivatives of a Function:
A derivative is referred to the instantaneous rate of change of a quantity with response to the other. It helps to look into the moment-by-moment nature of an amount. The derivative of a function is shown in the below-given formula.
Properties of Derivatives:
Read More: Limits and Derivatives