Limits of Standard Functions
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Limits, Continuity and Differentiability

79561 If \(f^{\prime}(2)=6, f^{\prime}(1)=4\), then
\(\lim _{h \rightarrow 0} \frac{f\left(2 h+2+h^{2}\right)-f(2)}{f\left(h+h^{2}+1\right)-f(1)}\) is equal to

1 3
2 \(-\frac{3}{2}\)
3 \(\frac{3}{2}\)
4 Does not exist
BCECE-2014
Limits, Continuity and Differentiability

79563 \(\lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin x \cos x}\) is equal to

1 \(\frac{2}{5}\)
2 \(\frac{3}{5}\)
3 \(\frac{3}{2}\)
4 \(\frac{3}{4}\)
BCECE-2009
Limits, Continuity and Differentiability

79565 If \(0\lt p\lt q\), then \(\lim _{n \rightarrow \infty}\left(q^{n}+p^{n}\right)^{1 / n}\) is equal to

1 e
2 \(p\)
3 \(\mathrm{q}\)
4 0
BCECE-2008
Limits, Continuity and Differentiability

79566 The value of \(\lim _{\alpha \rightarrow 0} \frac{{coses}^{-1}(\sec \alpha)+\cot ^{-1}(\tan \alpha)+\cot ^{-1} \cos \left(\sin ^{-1} \alpha\right)}{\alpha}\) is

1 0
2 -1
3 -2
4 1
BCECE-2007
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

79561 If \(f^{\prime}(2)=6, f^{\prime}(1)=4\), then
\(\lim _{h \rightarrow 0} \frac{f\left(2 h+2+h^{2}\right)-f(2)}{f\left(h+h^{2}+1\right)-f(1)}\) is equal to

1 3
2 \(-\frac{3}{2}\)
3 \(\frac{3}{2}\)
4 Does not exist
BCECE-2014
Limits, Continuity and Differentiability

79563 \(\lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin x \cos x}\) is equal to

1 \(\frac{2}{5}\)
2 \(\frac{3}{5}\)
3 \(\frac{3}{2}\)
4 \(\frac{3}{4}\)
BCECE-2009
Limits, Continuity and Differentiability

79565 If \(0\lt p\lt q\), then \(\lim _{n \rightarrow \infty}\left(q^{n}+p^{n}\right)^{1 / n}\) is equal to

1 e
2 \(p\)
3 \(\mathrm{q}\)
4 0
BCECE-2008
Limits, Continuity and Differentiability

79566 The value of \(\lim _{\alpha \rightarrow 0} \frac{{coses}^{-1}(\sec \alpha)+\cot ^{-1}(\tan \alpha)+\cot ^{-1} \cos \left(\sin ^{-1} \alpha\right)}{\alpha}\) is

1 0
2 -1
3 -2
4 1
BCECE-2007
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Limits, Continuity and Differentiability

79561 If \(f^{\prime}(2)=6, f^{\prime}(1)=4\), then
\(\lim _{h \rightarrow 0} \frac{f\left(2 h+2+h^{2}\right)-f(2)}{f\left(h+h^{2}+1\right)-f(1)}\) is equal to

1 3
2 \(-\frac{3}{2}\)
3 \(\frac{3}{2}\)
4 Does not exist
BCECE-2014
Limits, Continuity and Differentiability

79563 \(\lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin x \cos x}\) is equal to

1 \(\frac{2}{5}\)
2 \(\frac{3}{5}\)
3 \(\frac{3}{2}\)
4 \(\frac{3}{4}\)
BCECE-2009
Limits, Continuity and Differentiability

79565 If \(0\lt p\lt q\), then \(\lim _{n \rightarrow \infty}\left(q^{n}+p^{n}\right)^{1 / n}\) is equal to

1 e
2 \(p\)
3 \(\mathrm{q}\)
4 0
BCECE-2008
Limits, Continuity and Differentiability

79566 The value of \(\lim _{\alpha \rightarrow 0} \frac{{coses}^{-1}(\sec \alpha)+\cot ^{-1}(\tan \alpha)+\cot ^{-1} \cos \left(\sin ^{-1} \alpha\right)}{\alpha}\) is

1 0
2 -1
3 -2
4 1
BCECE-2007
For More Updates join with Us
Limits, Continuity and Differentiability

79561 If \(f^{\prime}(2)=6, f^{\prime}(1)=4\), then
\(\lim _{h \rightarrow 0} \frac{f\left(2 h+2+h^{2}\right)-f(2)}{f\left(h+h^{2}+1\right)-f(1)}\) is equal to

1 3
2 \(-\frac{3}{2}\)
3 \(\frac{3}{2}\)
4 Does not exist
BCECE-2014
Limits, Continuity and Differentiability

79563 \(\lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin x \cos x}\) is equal to

1 \(\frac{2}{5}\)
2 \(\frac{3}{5}\)
3 \(\frac{3}{2}\)
4 \(\frac{3}{4}\)
BCECE-2009
Limits, Continuity and Differentiability

79565 If \(0\lt p\lt q\), then \(\lim _{n \rightarrow \infty}\left(q^{n}+p^{n}\right)^{1 / n}\) is equal to

1 e
2 \(p\)
3 \(\mathrm{q}\)
4 0
BCECE-2008
Limits, Continuity and Differentiability

79566 The value of \(\lim _{\alpha \rightarrow 0} \frac{{coses}^{-1}(\sec \alpha)+\cot ^{-1}(\tan \alpha)+\cot ^{-1} \cos \left(\sin ^{-1} \alpha\right)}{\alpha}\) is

1 0
2 -1
3 -2
4 1
BCECE-2007