Differentiability and Continuity of Function
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Limits, Continuity and Differentiability

79952 For the function \(f(x)=\left\{\begin{array}{cc}\frac{e^{1 / x}-1}{e^{1 / x}+1} x \neq 0 \\ 0, x=0\end{array}\right.\), which of the following is correct:

1 \(\lim _{x \rightarrow 0} f(x)\) does not exist
2 \(\lim _{\mathrm{x} \rightarrow 0} f(\mathrm{x})=1\)
3 \(\lim _{\substack{\mathrm{x} \rightarrow 0 \\ \mathrm{x}=0}} f(\mathrm{x})\) exists but \(f(\mathrm{x})\) is not continuous at
4 \(f(\mathrm{x})\) is continuous at \(\mathrm{x}=0\)
UPSEE-2006
Limits, Continuity and Differentiability

79953 \(\lim _{x \rightarrow 0}(\operatorname{cosec} x)^{1 / \log x}\) is equal to:

1 0
2 1
3 \(1 / \mathrm{e}\)
4 None of these
UPSEE-2005
Limits, Continuity and Differentiability

79957 \(\lim _{x \rightarrow \frac{\pi}{2}}\left\{2 x \tan x-\frac{\pi}{\cos x}\right\}\) is

1 -3
2 -2
3 0
4 -1
UPSEE-2017
Limits, Continuity and Differentiability

79958 Given that \(f(0)=0\) and \(\lim _{x \rightarrow 0} \frac{f(x)}{x}\) exists, say \(L\). Here \(\boldsymbol{f}^{\prime}(0)\) denotes the derivative of \(\boldsymbol{f}\) w.r.t. \(\mathrm{x}\) at \(\mathbf{x}=\mathbf{0}\). Then \(\mathrm{L}\) is

1 \(2 f^{\prime}(0)-6\)
2 \(2 f^{\prime}(0)-5\)
3 \(f^{\prime}(0)\)
4 0
UPSEE-2017
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Limits, Continuity and Differentiability

79952 For the function \(f(x)=\left\{\begin{array}{cc}\frac{e^{1 / x}-1}{e^{1 / x}+1} x \neq 0 \\ 0, x=0\end{array}\right.\), which of the following is correct:

1 \(\lim _{x \rightarrow 0} f(x)\) does not exist
2 \(\lim _{\mathrm{x} \rightarrow 0} f(\mathrm{x})=1\)
3 \(\lim _{\substack{\mathrm{x} \rightarrow 0 \\ \mathrm{x}=0}} f(\mathrm{x})\) exists but \(f(\mathrm{x})\) is not continuous at
4 \(f(\mathrm{x})\) is continuous at \(\mathrm{x}=0\)
UPSEE-2006
Limits, Continuity and Differentiability

79953 \(\lim _{x \rightarrow 0}(\operatorname{cosec} x)^{1 / \log x}\) is equal to:

1 0
2 1
3 \(1 / \mathrm{e}\)
4 None of these
UPSEE-2005
Limits, Continuity and Differentiability

79957 \(\lim _{x \rightarrow \frac{\pi}{2}}\left\{2 x \tan x-\frac{\pi}{\cos x}\right\}\) is

1 -3
2 -2
3 0
4 -1
UPSEE-2017
Limits, Continuity and Differentiability

79958 Given that \(f(0)=0\) and \(\lim _{x \rightarrow 0} \frac{f(x)}{x}\) exists, say \(L\). Here \(\boldsymbol{f}^{\prime}(0)\) denotes the derivative of \(\boldsymbol{f}\) w.r.t. \(\mathrm{x}\) at \(\mathbf{x}=\mathbf{0}\). Then \(\mathrm{L}\) is

1 \(2 f^{\prime}(0)-6\)
2 \(2 f^{\prime}(0)-5\)
3 \(f^{\prime}(0)\)
4 0
UPSEE-2017
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

79952 For the function \(f(x)=\left\{\begin{array}{cc}\frac{e^{1 / x}-1}{e^{1 / x}+1} x \neq 0 \\ 0, x=0\end{array}\right.\), which of the following is correct:

1 \(\lim _{x \rightarrow 0} f(x)\) does not exist
2 \(\lim _{\mathrm{x} \rightarrow 0} f(\mathrm{x})=1\)
3 \(\lim _{\substack{\mathrm{x} \rightarrow 0 \\ \mathrm{x}=0}} f(\mathrm{x})\) exists but \(f(\mathrm{x})\) is not continuous at
4 \(f(\mathrm{x})\) is continuous at \(\mathrm{x}=0\)
UPSEE-2006
Limits, Continuity and Differentiability

79953 \(\lim _{x \rightarrow 0}(\operatorname{cosec} x)^{1 / \log x}\) is equal to:

1 0
2 1
3 \(1 / \mathrm{e}\)
4 None of these
UPSEE-2005
Limits, Continuity and Differentiability

79957 \(\lim _{x \rightarrow \frac{\pi}{2}}\left\{2 x \tan x-\frac{\pi}{\cos x}\right\}\) is

1 -3
2 -2
3 0
4 -1
UPSEE-2017
Limits, Continuity and Differentiability

79958 Given that \(f(0)=0\) and \(\lim _{x \rightarrow 0} \frac{f(x)}{x}\) exists, say \(L\). Here \(\boldsymbol{f}^{\prime}(0)\) denotes the derivative of \(\boldsymbol{f}\) w.r.t. \(\mathrm{x}\) at \(\mathbf{x}=\mathbf{0}\). Then \(\mathrm{L}\) is

1 \(2 f^{\prime}(0)-6\)
2 \(2 f^{\prime}(0)-5\)
3 \(f^{\prime}(0)\)
4 0
UPSEE-2017
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Limits, Continuity and Differentiability

79952 For the function \(f(x)=\left\{\begin{array}{cc}\frac{e^{1 / x}-1}{e^{1 / x}+1} x \neq 0 \\ 0, x=0\end{array}\right.\), which of the following is correct:

1 \(\lim _{x \rightarrow 0} f(x)\) does not exist
2 \(\lim _{\mathrm{x} \rightarrow 0} f(\mathrm{x})=1\)
3 \(\lim _{\substack{\mathrm{x} \rightarrow 0 \\ \mathrm{x}=0}} f(\mathrm{x})\) exists but \(f(\mathrm{x})\) is not continuous at
4 \(f(\mathrm{x})\) is continuous at \(\mathrm{x}=0\)
UPSEE-2006
Limits, Continuity and Differentiability

79953 \(\lim _{x \rightarrow 0}(\operatorname{cosec} x)^{1 / \log x}\) is equal to:

1 0
2 1
3 \(1 / \mathrm{e}\)
4 None of these
UPSEE-2005
Limits, Continuity and Differentiability

79957 \(\lim _{x \rightarrow \frac{\pi}{2}}\left\{2 x \tan x-\frac{\pi}{\cos x}\right\}\) is

1 -3
2 -2
3 0
4 -1
UPSEE-2017
Limits, Continuity and Differentiability

79958 Given that \(f(0)=0\) and \(\lim _{x \rightarrow 0} \frac{f(x)}{x}\) exists, say \(L\). Here \(\boldsymbol{f}^{\prime}(0)\) denotes the derivative of \(\boldsymbol{f}\) w.r.t. \(\mathrm{x}\) at \(\mathbf{x}=\mathbf{0}\). Then \(\mathrm{L}\) is

1 \(2 f^{\prime}(0)-6\)
2 \(2 f^{\prime}(0)-5\)
3 \(f^{\prime}(0)\)
4 0
UPSEE-2017
For More Updates join with Us