Limits of Standard Functions
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Limits, Continuity and Differentiability

79474 \(\sum_{r=1}^{n}(2 r-1)=x\), then
\(\lim _{n \rightarrow 0}\left[\frac{1^{3}}{x^{2}}+\frac{2^{3}}{x^{2}}+\frac{3^{3}}{x^{2}}+\ldots . .+\frac{n^{3}}{x^{2}}\right]=\)

1 \(\frac{1}{2}\)
2 1
3 \(\frac{1}{4}\)
4 4
Karnataka CET-2019
Limits, Continuity and Differentiability

79475 The value of \(\lim _{x \rightarrow 0} \frac{|x|}{x}\) is

1 1
2 -1
3 0
4 Does not exist
Karnataka CET-2018
Limits, Continuity and Differentiability

79476 If the function \(f(x)\) satisfies \(\lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\pi\), then \(\lim _{x \rightarrow 1} f(x)=\)

1 1
2 2
3 0
4 3
Karnataka CET-2014
Limits, Continuity and Differentiability

79480 \(\lim _{n \rightarrow \infty}\left\{n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}\right\}=\)

1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{3}\)
4 1
Limits, Continuity and Differentiability

79481 \(\lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=\)

1 \(\frac{2}{3}\)
2 \(\frac{2}{\sqrt{3}}\)
3 \(\frac{3 \sqrt{3}}{2}\)
4 \(\frac{2}{3 \sqrt{3}}\)
Karnataka CET-2011
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

79474 \(\sum_{r=1}^{n}(2 r-1)=x\), then
\(\lim _{n \rightarrow 0}\left[\frac{1^{3}}{x^{2}}+\frac{2^{3}}{x^{2}}+\frac{3^{3}}{x^{2}}+\ldots . .+\frac{n^{3}}{x^{2}}\right]=\)

1 \(\frac{1}{2}\)
2 1
3 \(\frac{1}{4}\)
4 4
Karnataka CET-2019
Limits, Continuity and Differentiability

79475 The value of \(\lim _{x \rightarrow 0} \frac{|x|}{x}\) is

1 1
2 -1
3 0
4 Does not exist
Karnataka CET-2018
Limits, Continuity and Differentiability

79476 If the function \(f(x)\) satisfies \(\lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\pi\), then \(\lim _{x \rightarrow 1} f(x)=\)

1 1
2 2
3 0
4 3
Karnataka CET-2014
Limits, Continuity and Differentiability

79480 \(\lim _{n \rightarrow \infty}\left\{n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}\right\}=\)

1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{3}\)
4 1
Limits, Continuity and Differentiability

79481 \(\lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=\)

1 \(\frac{2}{3}\)
2 \(\frac{2}{\sqrt{3}}\)
3 \(\frac{3 \sqrt{3}}{2}\)
4 \(\frac{2}{3 \sqrt{3}}\)
Karnataka CET-2011
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Limits, Continuity and Differentiability

79474 \(\sum_{r=1}^{n}(2 r-1)=x\), then
\(\lim _{n \rightarrow 0}\left[\frac{1^{3}}{x^{2}}+\frac{2^{3}}{x^{2}}+\frac{3^{3}}{x^{2}}+\ldots . .+\frac{n^{3}}{x^{2}}\right]=\)

1 \(\frac{1}{2}\)
2 1
3 \(\frac{1}{4}\)
4 4
Karnataka CET-2019
Limits, Continuity and Differentiability

79475 The value of \(\lim _{x \rightarrow 0} \frac{|x|}{x}\) is

1 1
2 -1
3 0
4 Does not exist
Karnataka CET-2018
Limits, Continuity and Differentiability

79476 If the function \(f(x)\) satisfies \(\lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\pi\), then \(\lim _{x \rightarrow 1} f(x)=\)

1 1
2 2
3 0
4 3
Karnataka CET-2014
Limits, Continuity and Differentiability

79480 \(\lim _{n \rightarrow \infty}\left\{n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}\right\}=\)

1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{3}\)
4 1
Limits, Continuity and Differentiability

79481 \(\lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=\)

1 \(\frac{2}{3}\)
2 \(\frac{2}{\sqrt{3}}\)
3 \(\frac{3 \sqrt{3}}{2}\)
4 \(\frac{2}{3 \sqrt{3}}\)
Karnataka CET-2011
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Limits, Continuity and Differentiability

79474 \(\sum_{r=1}^{n}(2 r-1)=x\), then
\(\lim _{n \rightarrow 0}\left[\frac{1^{3}}{x^{2}}+\frac{2^{3}}{x^{2}}+\frac{3^{3}}{x^{2}}+\ldots . .+\frac{n^{3}}{x^{2}}\right]=\)

1 \(\frac{1}{2}\)
2 1
3 \(\frac{1}{4}\)
4 4
Karnataka CET-2019
Limits, Continuity and Differentiability

79475 The value of \(\lim _{x \rightarrow 0} \frac{|x|}{x}\) is

1 1
2 -1
3 0
4 Does not exist
Karnataka CET-2018
Limits, Continuity and Differentiability

79476 If the function \(f(x)\) satisfies \(\lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\pi\), then \(\lim _{x \rightarrow 1} f(x)=\)

1 1
2 2
3 0
4 3
Karnataka CET-2014
Limits, Continuity and Differentiability

79480 \(\lim _{n \rightarrow \infty}\left\{n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}\right\}=\)

1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{3}\)
4 1
Limits, Continuity and Differentiability

79481 \(\lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=\)

1 \(\frac{2}{3}\)
2 \(\frac{2}{\sqrt{3}}\)
3 \(\frac{3 \sqrt{3}}{2}\)
4 \(\frac{2}{3 \sqrt{3}}\)
Karnataka CET-2011
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

79474 \(\sum_{r=1}^{n}(2 r-1)=x\), then
\(\lim _{n \rightarrow 0}\left[\frac{1^{3}}{x^{2}}+\frac{2^{3}}{x^{2}}+\frac{3^{3}}{x^{2}}+\ldots . .+\frac{n^{3}}{x^{2}}\right]=\)

1 \(\frac{1}{2}\)
2 1
3 \(\frac{1}{4}\)
4 4
Karnataka CET-2019
Limits, Continuity and Differentiability

79475 The value of \(\lim _{x \rightarrow 0} \frac{|x|}{x}\) is

1 1
2 -1
3 0
4 Does not exist
Karnataka CET-2018
Limits, Continuity and Differentiability

79476 If the function \(f(x)\) satisfies \(\lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\pi\), then \(\lim _{x \rightarrow 1} f(x)=\)

1 1
2 2
3 0
4 3
Karnataka CET-2014
Limits, Continuity and Differentiability

79480 \(\lim _{n \rightarrow \infty}\left\{n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}\right\}=\)

1 \(\frac{2 \pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{3}\)
4 1
Limits, Continuity and Differentiability

79481 \(\lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=\)

1 \(\frac{2}{3}\)
2 \(\frac{2}{\sqrt{3}}\)
3 \(\frac{3 \sqrt{3}}{2}\)
4 \(\frac{2}{3 \sqrt{3}}\)
Karnataka CET-2011