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AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\left\{\begin{array}{cl}x^\alpha \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$

which of the following is true?

A
$f(x)$ is continuous and differentiable if $0 \leq \alpha<1$
B
$f(x)$ is discontinuous and not differentiable if $0 \leq \alpha<1$
C
$f(x)$ is continuous and differentiable for $\alpha>1$
D
$f(x)$ is discontinuous and differentiable for $\alpha>1$
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Let $f(x)=\min \left\{x, x^2\right\}$ for every real number of $x$, then
A
$f(x)$ is continuous for all $x$
B
$f(x)$ is differentiable for all $x$
C
$f(x)=2$ for all $x>1$
D
$f(x)$ is not differentiable at three values of $x$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{x \rightarrow 0} \frac{1-\cos x \cdot \cos 2 x}{\sin ^2 x}=$
A
$\frac{11}{4}$
B
$\frac{5}{2}$
C
3
D
5
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{x \rightarrow-1}\left(\frac{3 x^2-2 x+3}{3 x^2+x-2}\right)^{3 x-2}=$
A
-3
B
$e^{-1}$
C
$e^{-3}$
D
-1
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