1
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\lim \limits_{x \rightarrow 0} \frac{e^x-a-\log (1+x)}{\sin x}=0$, then $a=$
A
2
B
0
C
-1
D
1
2
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The values of $a$ and $b$ for which the function

$ f(x)=\left\{\begin{array}{cl}1+|\sin x|^{\frac{a}{\sin x \mid}} & \frac{-\pi}{6} < x < 0 \\ b, & x=0 \quad \text { is continuous at } x=0 \\ e^{\frac{\tan 2 x}{\tan 3 x},} & 0 < x < \frac{\pi}{6}\end{array}\right. $

are

A
$a=1, b=\frac{2}{3}$
B
$a=\frac{2}{3}, b=e^{\frac{2}{3}}$
C
$a=\frac{2}{3}, b=\frac{3}{2}$
D
$a=-1, b=e^{\frac{2}{3}}$
3
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\left\{\begin{array}{cc}2 x+3, & x \leq 1 \\ a x^2+b x, & x>1\end{array}\right.$

is differentiable, $\forall x \in R$, then $f^{\prime}(2)=$

A
5
B
4
C
-4
D
-10
4
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=t^2+t^3$ and $x=t-t^4$, then $\frac{d^2 y}{d x^2}$ at $t=1$ is
A
$\frac{-2}{3}$
B
$\frac{-4}{3}$
C
$\frac{8}{3}$
D
4
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