Differentiability and Continuity of Function
Limits, Continuity and Differentiability

79996 If \(f(x)=\left\{\begin{array}{ll}-x-\pi / 2 & x \leq-\pi / 2 \\ -\cos x & -\pi / 2\lt x \leq 0 \\ x-1 & 0\lt x \leq 1 \\ \ln x & x>1\end{array}\right.\), then

1 \(f(x)\) is continuous at \(x=-\pi / 2\)
2 \(f(x)\) is differentiable at \(x=0\)
3 \(f(x)\) is not differentiable at \(x=1\)
4 \(f(x)\) is not differentiable at \(x=-3 / 2\)
Limits, Continuity and Differentiability

79997 Let \(f(x)=\left\{\begin{array}{c}|x|,-\infty\lt x\lt 2 \\ |2 x-4|, 2 \leq x \leq 20\end{array}\right.\)
\(x=a\) is a point where \(f(x)\) is continuous but not differentiable and \(x=b\) is a point where \(f(x)\) is not differentiable \((a \neq b)\). Then \(a+b=\)

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

79998 The number of discontinuities in \(R\) for the
function \(f(x)=\frac{x-1}{x^{3}+6 x^{2}+11 x+6}\) is

1 3
2 2
3 1
4 0
Limits, Continuity and Differentiability

79999 \(f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & \text { when } x\lt 0 \\ 5 x^2+a, & \text { when } 0 \leq x \leq 1 \\ b\left(\frac{x^2-1}{x^2-3 x+2}\right), & \text { when } 1\lt x\lt 3 \\ -14, & \text { when } x>3\end{array}\right.\) is a
continuous function on \(R\), the \((a, b)\) =

1 \(\left(2, \frac{-7}{2}\right)\)
2 \((2,-14)\)
3 \(\left(\frac{-7}{2},-14\right)\)
4 \((2,7)\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Limits, Continuity and Differentiability

79996 If \(f(x)=\left\{\begin{array}{ll}-x-\pi / 2 & x \leq-\pi / 2 \\ -\cos x & -\pi / 2\lt x \leq 0 \\ x-1 & 0\lt x \leq 1 \\ \ln x & x>1\end{array}\right.\), then

1 \(f(x)\) is continuous at \(x=-\pi / 2\)
2 \(f(x)\) is differentiable at \(x=0\)
3 \(f(x)\) is not differentiable at \(x=1\)
4 \(f(x)\) is not differentiable at \(x=-3 / 2\)
Limits, Continuity and Differentiability

79997 Let \(f(x)=\left\{\begin{array}{c}|x|,-\infty\lt x\lt 2 \\ |2 x-4|, 2 \leq x \leq 20\end{array}\right.\)
\(x=a\) is a point where \(f(x)\) is continuous but not differentiable and \(x=b\) is a point where \(f(x)\) is not differentiable \((a \neq b)\). Then \(a+b=\)

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

79998 The number of discontinuities in \(R\) for the
function \(f(x)=\frac{x-1}{x^{3}+6 x^{2}+11 x+6}\) is

1 3
2 2
3 1
4 0
Limits, Continuity and Differentiability

79999 \(f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & \text { when } x\lt 0 \\ 5 x^2+a, & \text { when } 0 \leq x \leq 1 \\ b\left(\frac{x^2-1}{x^2-3 x+2}\right), & \text { when } 1\lt x\lt 3 \\ -14, & \text { when } x>3\end{array}\right.\) is a
continuous function on \(R\), the \((a, b)\) =

1 \(\left(2, \frac{-7}{2}\right)\)
2 \((2,-14)\)
3 \(\left(\frac{-7}{2},-14\right)\)
4 \((2,7)\)
Limits, Continuity and Differentiability

79996 If \(f(x)=\left\{\begin{array}{ll}-x-\pi / 2 & x \leq-\pi / 2 \\ -\cos x & -\pi / 2\lt x \leq 0 \\ x-1 & 0\lt x \leq 1 \\ \ln x & x>1\end{array}\right.\), then

1 \(f(x)\) is continuous at \(x=-\pi / 2\)
2 \(f(x)\) is differentiable at \(x=0\)
3 \(f(x)\) is not differentiable at \(x=1\)
4 \(f(x)\) is not differentiable at \(x=-3 / 2\)
Limits, Continuity and Differentiability

79997 Let \(f(x)=\left\{\begin{array}{c}|x|,-\infty\lt x\lt 2 \\ |2 x-4|, 2 \leq x \leq 20\end{array}\right.\)
\(x=a\) is a point where \(f(x)\) is continuous but not differentiable and \(x=b\) is a point where \(f(x)\) is not differentiable \((a \neq b)\). Then \(a+b=\)

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

79998 The number of discontinuities in \(R\) for the
function \(f(x)=\frac{x-1}{x^{3}+6 x^{2}+11 x+6}\) is

1 3
2 2
3 1
4 0
Limits, Continuity and Differentiability

79999 \(f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & \text { when } x\lt 0 \\ 5 x^2+a, & \text { when } 0 \leq x \leq 1 \\ b\left(\frac{x^2-1}{x^2-3 x+2}\right), & \text { when } 1\lt x\lt 3 \\ -14, & \text { when } x>3\end{array}\right.\) is a
continuous function on \(R\), the \((a, b)\) =

1 \(\left(2, \frac{-7}{2}\right)\)
2 \((2,-14)\)
3 \(\left(\frac{-7}{2},-14\right)\)
4 \((2,7)\)
Limits, Continuity and Differentiability

79996 If \(f(x)=\left\{\begin{array}{ll}-x-\pi / 2 & x \leq-\pi / 2 \\ -\cos x & -\pi / 2\lt x \leq 0 \\ x-1 & 0\lt x \leq 1 \\ \ln x & x>1\end{array}\right.\), then

1 \(f(x)\) is continuous at \(x=-\pi / 2\)
2 \(f(x)\) is differentiable at \(x=0\)
3 \(f(x)\) is not differentiable at \(x=1\)
4 \(f(x)\) is not differentiable at \(x=-3 / 2\)
Limits, Continuity and Differentiability

79997 Let \(f(x)=\left\{\begin{array}{c}|x|,-\infty\lt x\lt 2 \\ |2 x-4|, 2 \leq x \leq 20\end{array}\right.\)
\(x=a\) is a point where \(f(x)\) is continuous but not differentiable and \(x=b\) is a point where \(f(x)\) is not differentiable \((a \neq b)\). Then \(a+b=\)

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

79998 The number of discontinuities in \(R\) for the
function \(f(x)=\frac{x-1}{x^{3}+6 x^{2}+11 x+6}\) is

1 3
2 2
3 1
4 0
Limits, Continuity and Differentiability

79999 \(f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & \text { when } x\lt 0 \\ 5 x^2+a, & \text { when } 0 \leq x \leq 1 \\ b\left(\frac{x^2-1}{x^2-3 x+2}\right), & \text { when } 1\lt x\lt 3 \\ -14, & \text { when } x>3\end{array}\right.\) is a
continuous function on \(R\), the \((a, b)\) =

1 \(\left(2, \frac{-7}{2}\right)\)
2 \((2,-14)\)
3 \(\left(\frac{-7}{2},-14\right)\)
4 \((2,7)\)