1
COMEDK 2024 Morning Shift
+1
-0

$$\text { If } f(x)=\left\{\begin{array}{cc} \frac{1-\sin x}{(\pi-2 x)^2} & , \quad \text { if } x \neq \frac{\pi}{2} \\ \lambda, & \text { if } x=\frac{\pi}{2} \end{array}\right.$$

Then $$f(x)$$ will be continues function at $$x=\frac{\pi}{2}$$, then $$\lambda=$$

A
$$-\frac{1}{8}$$
B
1
C
$$\frac{1}{4}$$
D
$$\frac{1}{8}$$
2
COMEDK 2024 Morning Shift
+1
-0

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to

A
$$a^{-\frac{3}{2}}$$
B
$$\frac{1}{2 a^{\frac{3}{2}}}$$
C
$$\frac{1}{2}$$
D
$$2 a^{-\frac{3}{2}}$$
3
COMEDK 2024 Morning Shift
+1
-0

$$\lim _\limits{x \rightarrow 0}\left(\frac{\sin a x}{\sin b x}\right)^k \text { equals }$$

A
$$\left(\frac{b}{a}\right)^k$$
B
$$\left(\frac{a}{b}\right)^k$$
C
$$\frac{a}{b}$$
D
$$\frac{b}{a}$$
4
COMEDK 2023 Morning Shift
+1
-0

The value of $$\lim _\limits{x \rightarrow 0} \frac{e^{a x}-e^{b x}}{2 x}$$ is equal to

A
$$\frac{a+b}{2}$$
B
$$\frac{a-b}{2}$$
C
$$\frac{e^{a b}}{2}$$
D
0
EXAM MAP
Medical
NEET