Get Answers to all your Questions

header-bg qa

 If f(x) is continuous at x=0 and f(0)=2, then  \mathrm{\lim _{x \rightarrow 0} \frac{\int_0^x f(x) d u}{x}}  is

Option: 1

0


Option: 2

2


Option: 3

f(2)


Option: 4

none of these


Answers (1)

best_answer

Since  f(x)  is continuous at  x=0 , therefore 

\mathrm{ \lim _{x \rightarrow 0} f(x)=f(0) \Rightarrow f(0)=2 }
Now, \mathrm{ \lim _{x \rightarrow 0} \frac{\int_0^x f(u) d u}{x}=\lim _{x \rightarrow 0} \frac{f(x)}{1}\left[\begin{array}{c}\text { Using L' Hospital 'S Rule } \\ \because f(x) \text { is continuous at } x=0\end{array}\right]=f(0)=2 }

Posted by

Deependra Verma

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE