1
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $f(x)=\left\{\begin{array}{cl}0, & x=0 \\ 2-x, & \text { for } 0 < x < 1 \\ 2, & \text { for } x=1 \\ \frac{1}{2}-x, & \text { for } 1 < x < 2 \\ \frac{-3}{2}, & \text { for } x \geq 2\end{array}\right.$

then which of the following is true

A

$f$ is right continuous at $x=0$

B

$f$ is left continuous at $x=1$

C

$f$ is right continuous at $x=1$

D

$f$ is continuous at $x=2$

2
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left(\frac{1+x}{1-x}\right)^{\frac{1}{x}}$ is continuous at $x=0$, then $f(0)=$
A
$e^{\frac{1}{2}}$
B
$e^2$
C
$e^{-2}$
D
$e^{\frac{-1}{2}}$
3
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The function $f(x)=|x-24|$ is
A
Differentiable on $[0,25]$
B
not continuous at $x=24$
C
neither continuous nor differentiable on $[0,25]$
D
Continuous on $[0,25]$ but not differentiable on $[0,25]$
4
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \infty}}}$, then the value of $\frac{d^2 y}{d x^2}$ at the point $(\pi, 1)$ is

A
2
B
-2
C
$-\frac{1}{2}$
D
$\frac{1}{2}$
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