If [.] is greatest integer function and \( n \) is a positive integer, then \( \lim _{x \rightar...
If [.] is greatest integer function and \( n \) is a positive integer, then \( \lim _{x \rightarrow 0}\left(\left[\frac{n x}{\sin x}\right]+\left[\frac{n \tan x}{x}\right]\right)= \)
(a) \( 2 n \)
(b) 2
(c) \( 2 n-1 \)
(d) \( 2 n+2 \)
๐ฒPW App Link - https://bit.ly/YTAI_PWAP
๐PW Website - https://www.pw.live
Other Videos By PW Solutions
2023-06-08 | \( \lim _{x \rightarrow 0} \frac{\sin x^{4}-x^{4} \cos x^{4}+x^{20}}{x^{4}\left(e^{2 x^{4}}-1-2 ... |
2023-06-08 | \( \lim _{x \rightarrow 0}(x)^{\frac{1}{\ln \sin x}} \) is equal to
(a) 1
(b) 0
(c) \( e \)
(d) ... |
2023-06-08 | Let \( a, b \) be constants such that \( \lim _{x \rightarrow 1} \frac{x^{2}+a x+b}{(\ln (2-x))^... |
2023-06-08 | \[
\lim _{t \rightarrow \infty} \frac{\sqrt{2 t^{2}-t-1}-\sqrt{t^{2}-t+1}}{t(\tan \pi / 8)}
\]
(... |
2023-06-08 | \[
\lim _{x \rightarrow 0^{+}}\left(\ln \left(\sin ^{3} x\right)-\ln \left(x^{4}+e x^{3}\right)\... |
2023-06-08 | \( x^{5}+p x+r=0, x_{1}, x_{2}, x_{3}, x_{4} \) and \( x_{5} \) are the roots of the equation th... |
2023-06-08 | Evalute \( \lim _{x \rightarrow 0}\left[\frac{a \sin x}{x}\right]+\left[\frac{b \tan x}{x}\right... |
2023-06-08 | \[
\lim _{n \rightarrow \infty} \frac{1}{n^{2}} \prod_{r=2}^{n}\left(\frac{r+1}{r-1}\right)
\]
(... |
2023-06-08 | Which of the following is/are true.
(a) If \( \lim _{x \rightarrow a}\{f(x)+g(x)\} \) exists, th... |
2023-06-08 | If \( \lim _{x \rightarrow 1} \frac{\frac{\pi}{4}-\tan ^{-1} x}{e^{\sin (\ln x)}-x^{n}} \) exist... |
2023-06-08 | If [.] is greatest integer function and \( n \) is a positive integer, then \( \lim _{x \rightar... |
2023-06-08 | Evaluate \( \lim _{n \rightarrow \infty} \frac{[x]+[4 x]+[7 x]+\ldots+[(3 n-2) x]}{n^{2}} \) whe... |
2023-06-08 | \[
\lim _{x \rightarrow 0} \frac{e^{x^{2}}-\cos x}{x^{2}}
\]
(a) 0.5
(b) 1
(c) 1.5
(d) Does not ... |
2023-06-08 | \( \lim _{n \rightarrow \infty} \frac{n^{p} \sin ^{2}(n !)}{n+1}, 0p1 \), is equal to
(a) 0
(b) ... |
2023-06-08 | If \( \lim _{x \rightarrow 4} \frac{f(x)-5}{x-2}=3 \) then \( \lim _{x \rightarrow 4} f(x) \)
(a... |
2023-06-08 | \( \lim _{x \rightarrow \infty} \frac{\ln x^{n}-[x]}{[x]}, n \in N \), is \( ([\cdot] \) denotes... |
2023-06-08 | If \( \lim _{x \rightarrow \infty}\left(\sqrt{x^{4}+a x^{3}+3 x^{2}+b x+2}\right. \) \( \left.-\... |
2023-06-08 | \[
\lim _{n \rightarrow \infty} \frac{n^{2}}{3} \prod_{r=2}^{n}\left(\frac{r^{2}-r+1}{r^{2}+r+1}... |
2023-06-08 | Evaluate \( \lim _{x \rightarrow \infty} \frac{4 x+3}{x-8} \) (a) 4 (b) 1 (c) 3 |
2023-06-08 | \[
\lim _{x \rightarrow 0}\left[\frac{1}{x}-\frac{\ln (1+x)}{x^{2}}\right]=
\]
(a) \( 1 / 2 \)
(... |
2023-06-08 | Let \( f: R \rightarrow R \) be a positive increasing function with \( \lim _{x \rightarrow \inf... |