If [cdot] denotes the greatest integer functi | vedclass

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

Question

(A) We are given the limit: $\lim _{x \rightarrow \frac{-3}{5}} \frac{1}{x}\left[\frac{-1}{x}\right]$.As $x \rightarrow \frac{-3}{5}$,the term $\frac{

Vedclass · Accepted Answer

$\frac{-5}{3}$

Vedclass · Answer

(A) We are given the limit: $\lim _{x ightarrow \frac{-3}{5}} \frac{1}{x}\left[\frac{-1}{x}ight]$.As $x ightarrow \frac{-3}{5}$,the term $\frac{-1}{x} ightarrow \frac{-1}{-3/5} = \frac{5}{3}$.Since $\frac{5}{3} = 1.66...$,it lies in the interval $[1, 2)$.By the definition of the greatest integer function,$[\frac{5}{3}] = 1$.Substituting these values into the expression,we get:$\lim _{x}$ ${ightarrow \frac{-3}{5}} \frac{1}{x}\left[\frac{-1}{x}ight] = \left(\frac{1}{-3/5}ight) 	imes [\frac{5}{3}] = \frac{-5}{3} 	imes 1 = \frac{-5}{3}$.

If $[\cdot]$ denotes the greatest integer function,then $\lim _{x \rightarrow \frac{-3}{5}} \frac{1}{x}\left[\frac{-1}{x}\right]=$

Similar Questions

$\mathop {\lim }\limits_{x \to 3} \left\{ {\frac{{x - 3}}{{\sqrt {x - 2} - \sqrt {4 - x} }}} \right\} = $

$\mathop {\lim }\limits_{m \to \infty } {\left( {\cos \frac{x}{m}} \right)^m} = $

$\lim _{z \rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1} = $

$\mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {3x} - 3}}{{\sqrt {2x - 4} - \sqrt 2 }}$ is equal to

If $A \neq 0$ and $x > 0$,then $\lim _{n \rightarrow \infty} \frac{\cos x - e^{nx}}{1 - A e^{nx}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module