Question:
$\displaystyle \lim_{x \to 0} $ $\frac{\left(1+2x\right)^{10}-1}{x}$ is equal to
$\displaystyle \lim_{x \to 0} $ $\frac{\left(1+2x\right)^{10}-1}{x}$ is equal to
Updated On: Jun 6, 2022
- $5$
- $10$
- $15$
- $20$
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The Correct Option is D
Solution and Explanation
$\displaystyle\lim _{x \rightarrow 0} \frac{(1+2 x)^{10}-1}{x} $ $(\frac{0}{0}$ form )
Using L' hospital rule,
$=\displaystyle\lim _{x \rightarrow 0} \frac{10(1+2 x)^{9}(2)-0}{1} $
$=10(1+0)^{9} \cdot 2=20$
Using L' hospital rule,
$=\displaystyle\lim _{x \rightarrow 0} \frac{10(1+2 x)^{9}(2)-0}{1} $
$=10(1+0)^{9} \cdot 2=20$
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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