Let [x] denote the greatest integer less than | vedclass

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

Question

(A) Given $f(x) = 2x - [2x]$.To find $l_1 = \lim_{x \rightarrow 2^{-}} f(x)$:Let $x = 2 - h$,where $h \rightarrow 0$ and $h > 0$.$l_1 = \lim_{h \right

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Given $f(x) = 2x - [2x]$.To find $l_1 = \lim_{x \rightarrow 2^{-}} f(x)$:Let $x = 2 - h$,where $h \rightarrow 0$ and $h > 0$.$l_1 = \lim_{h \rightarrow 0} (2(2 - h) - [2(2 - h)]) = \lim_{h \rightarrow 0} (4 - 2h - [4 - 2h])$.Since $h$ is a very small positive number,$4 - 2h$ is slightly less than $4$,so $[4 - 2h] = 3$.Thus,$l_1 = 4 - 3 = 1$.To find $l_2 = \lim_{x \rightarrow 2^{+}} f(x)$:Let $x = 2 + h$,where $h \rightarrow 0$ and $h > 0$.$l_2 = \lim_{h \rightarrow 0} (2(2 + h) - [2(2 + h)]) = \lim_{h \rightarrow 0} (4 + 2h - [4 + 2h])$.Since $h$ is a very small positive number,$4 + 2h$ is slightly greater than $4$,so $[4 + 2h] = 4$.Thus,$l_2 = 4 - 4 = 0$.Therefore,$l_1 + l_2 = 1 + 0 = 1$.

Let $[x]$ denote the greatest integer less than or equal to $x$ and $f(x) = 2x - [2x]$. If $\lim_{x \rightarrow 2^{-}} f(x) = l_1$ and $\lim_{x \rightarrow 2^{+}} f(x) = l_2$,then $l_1 + l_2 =$

Similar Questions

The value of $\mathop {\lim }\limits_{x \to 0} \left( \left[ \frac{100x}{\sin x} \right] + \left[ \frac{99 \sin x}{x} \right] \right)$,where $[.]$ denotes the greatest integer function,is

$\lim _{x \rightarrow 0} \frac{(1-e^x) \sin x}{x^2+x^3}$ is equal to

$\lim _{x \rightarrow 0}\left(\frac{\sinh 2 x}{2 x}\right)^{\frac{1}{x^2}} = $

The value of $\lim _{n \rightarrow \infty} n \sin \frac{2 \pi}{3 n} \cos \frac{2 \pi}{3 n}$ is

Let $f(x)=5-|x-2|$ and $g(x)=|x+1|, x \in R$. If $f(x)$ attains its maximum value at $\alpha$ and $g(x)$ attains its minimum value at $\beta$,then $\lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^2-5 x+6\right)}{x^2-6 x+8}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module