lim _{x rightarrow 0} left( frac{x cdot 10^x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given limit: $L = \lim _{x \rightarrow 0} \frac{x(10^x - 1)}{1 - \cos x}$.Since this is a $\frac{0}{0}$ form,we apply $L$-Hospital's rule:$L = \li

Vedclass · Accepted Answer

$2 \log 10$

Vedclass · Answer

(B) Given limit: $L = \lim _{x \rightarrow 0} \frac{x(10^x - 1)}{1 - \cos x}$.Since this is a $\frac{0}{0}$ form,we apply $L$-Hospital's rule:$L = \lim _{x \rightarrow 0} \frac{x \cdot 10^x \ln 10 + (10^x - 1)}{\sin x}$.Again,this is a $\frac{0}{0}$ form,so we apply $L$-Hospital's rule again:$L = \lim _{x \rightarrow 0} \frac{x \cdot 10^x (\ln 10)^2 + 10^x \ln 10 + 10^x \ln 10}{\cos x}$.Substituting $x = 0$:$L = \frac{0 \cdot 10^0 (\ln 10)^2 + 10^0 \ln 10 + 10^0 \ln 10}{\cos 0} = \frac{0 + \ln 10 + \ln 10}{1} = 2 \ln 10 = 2 \log_{e} 10$.Note: In the context of the options provided,$\log 10$ refers to $\ln 10$ (natural logarithm).

$\lim _{x \rightarrow 0} \left( \frac{x \cdot 10^x - x}{1 - \cos x} \right)$ is equal to

Similar Questions

Assertion: The isothermal curves intersect each other at a certain point.
Reason: The isothermal change takes place slowly,so,the isothermal curves have very little slope.

Compared to other countries,which industry has received less attention for development in India?

Who was the first scientist to use the term 'virus' as a pathogen of infectious diseases?

Two ions having masses in the ratio $1: 1$ and charges $1: 2$ are projected into a uniform magnetic field perpendicular to the field with speeds in the ratio $2: 3$. The ratio of the radii of circular paths along which the two particles move is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module