Limits of Standard Functions
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Limits, Continuity and Differentiability

79554 If \(\lim _{x \rightarrow 0} \frac{\{(a-n) n x-\tan x\} \sin n x}{x^{2}}=0\), where \(n\) is a non-zero real number, then a is equal to

1 0
2 \(\frac{\mathrm{n}+1}{\mathrm{n}}\)
3 \(\mathrm{n}\)
4 \(n+\frac{1}{n}\)
[JCECE-2016]
Limits, Continuity and Differentiability

79555 \(\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}\) is equal to

1 \(\frac{1}{2}\)
2 0
3 1
4 2
BCECE-2018
Limits, Continuity and Differentiability

79556 \(\lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\frac{2 x+1}{x-1}\right)^{x}\right\}}\) is equal to

1 1
2 0
3 \(\frac{\pi}{2}\)
4 Non-existent
BCECE-2017
Limits, Continuity and Differentiability

79558 The value of \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^{2} \sin 3 x}\) equal to

1 \(\frac{10}{3}\)
2 \(\frac{3}{10}\)
3 \(\frac{6}{5}\)
4 \(\frac{5}{6}\)
BCECE-2016
Limits, Continuity and Differentiability

79559 The value of \(\lim _{x \rightarrow 0} \frac{e^{x}+\log (1+x)-(1-x)^{-2}}{x^{2}}\) is
equal to

1 0
2 -3
3 -1
4 Infinity
BCECE-2016
Join With Us for More Updates
Limits, Continuity and Differentiability

79554 If \(\lim _{x \rightarrow 0} \frac{\{(a-n) n x-\tan x\} \sin n x}{x^{2}}=0\), where \(n\) is a non-zero real number, then a is equal to

1 0
2 \(\frac{\mathrm{n}+1}{\mathrm{n}}\)
3 \(\mathrm{n}\)
4 \(n+\frac{1}{n}\)
[JCECE-2016]
Limits, Continuity and Differentiability

79555 \(\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}\) is equal to

1 \(\frac{1}{2}\)
2 0
3 1
4 2
BCECE-2018
Limits, Continuity and Differentiability

79556 \(\lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\frac{2 x+1}{x-1}\right)^{x}\right\}}\) is equal to

1 1
2 0
3 \(\frac{\pi}{2}\)
4 Non-existent
BCECE-2017
Limits, Continuity and Differentiability

79558 The value of \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^{2} \sin 3 x}\) equal to

1 \(\frac{10}{3}\)
2 \(\frac{3}{10}\)
3 \(\frac{6}{5}\)
4 \(\frac{5}{6}\)
BCECE-2016
Limits, Continuity and Differentiability

79559 The value of \(\lim _{x \rightarrow 0} \frac{e^{x}+\log (1+x)-(1-x)^{-2}}{x^{2}}\) is
equal to

1 0
2 -3
3 -1
4 Infinity
BCECE-2016
For More Updates join with Us
Limits, Continuity and Differentiability

79554 If \(\lim _{x \rightarrow 0} \frac{\{(a-n) n x-\tan x\} \sin n x}{x^{2}}=0\), where \(n\) is a non-zero real number, then a is equal to

1 0
2 \(\frac{\mathrm{n}+1}{\mathrm{n}}\)
3 \(\mathrm{n}\)
4 \(n+\frac{1}{n}\)
[JCECE-2016]
Limits, Continuity and Differentiability

79555 \(\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}\) is equal to

1 \(\frac{1}{2}\)
2 0
3 1
4 2
BCECE-2018
Limits, Continuity and Differentiability

79556 \(\lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\frac{2 x+1}{x-1}\right)^{x}\right\}}\) is equal to

1 1
2 0
3 \(\frac{\pi}{2}\)
4 Non-existent
BCECE-2017
Limits, Continuity and Differentiability

79558 The value of \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^{2} \sin 3 x}\) equal to

1 \(\frac{10}{3}\)
2 \(\frac{3}{10}\)
3 \(\frac{6}{5}\)
4 \(\frac{5}{6}\)
BCECE-2016
Limits, Continuity and Differentiability

79559 The value of \(\lim _{x \rightarrow 0} \frac{e^{x}+\log (1+x)-(1-x)^{-2}}{x^{2}}\) is
equal to

1 0
2 -3
3 -1
4 Infinity
BCECE-2016
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

79554 If \(\lim _{x \rightarrow 0} \frac{\{(a-n) n x-\tan x\} \sin n x}{x^{2}}=0\), where \(n\) is a non-zero real number, then a is equal to

1 0
2 \(\frac{\mathrm{n}+1}{\mathrm{n}}\)
3 \(\mathrm{n}\)
4 \(n+\frac{1}{n}\)
[JCECE-2016]
Limits, Continuity and Differentiability

79555 \(\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}\) is equal to

1 \(\frac{1}{2}\)
2 0
3 1
4 2
BCECE-2018
Limits, Continuity and Differentiability

79556 \(\lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\frac{2 x+1}{x-1}\right)^{x}\right\}}\) is equal to

1 1
2 0
3 \(\frac{\pi}{2}\)
4 Non-existent
BCECE-2017
Limits, Continuity and Differentiability

79558 The value of \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^{2} \sin 3 x}\) equal to

1 \(\frac{10}{3}\)
2 \(\frac{3}{10}\)
3 \(\frac{6}{5}\)
4 \(\frac{5}{6}\)
BCECE-2016
Limits, Continuity and Differentiability

79559 The value of \(\lim _{x \rightarrow 0} \frac{e^{x}+\log (1+x)-(1-x)^{-2}}{x^{2}}\) is
equal to

1 0
2 -3
3 -1
4 Infinity
BCECE-2016
Join With Us for More Updates
Limits, Continuity and Differentiability

79554 If \(\lim _{x \rightarrow 0} \frac{\{(a-n) n x-\tan x\} \sin n x}{x^{2}}=0\), where \(n\) is a non-zero real number, then a is equal to

1 0
2 \(\frac{\mathrm{n}+1}{\mathrm{n}}\)
3 \(\mathrm{n}\)
4 \(n+\frac{1}{n}\)
[JCECE-2016]
Limits, Continuity and Differentiability

79555 \(\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}\) is equal to

1 \(\frac{1}{2}\)
2 0
3 1
4 2
BCECE-2018
Limits, Continuity and Differentiability

79556 \(\lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\frac{2 x+1}{x-1}\right)^{x}\right\}}\) is equal to

1 1
2 0
3 \(\frac{\pi}{2}\)
4 Non-existent
BCECE-2017
Limits, Continuity and Differentiability

79558 The value of \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^{2} \sin 3 x}\) equal to

1 \(\frac{10}{3}\)
2 \(\frac{3}{10}\)
3 \(\frac{6}{5}\)
4 \(\frac{5}{6}\)
BCECE-2016
Limits, Continuity and Differentiability

79559 The value of \(\lim _{x \rightarrow 0} \frac{e^{x}+\log (1+x)-(1-x)^{-2}}{x^{2}}\) is
equal to

1 0
2 -3
3 -1
4 Infinity
BCECE-2016