1
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
$$\frac{b}{a}$$
2
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
3
COMEDK 2023 Morning Shift
+1
-0

If $$f(x) = \left\{ {\matrix{ {2\sin x} & ; & { - \pi \le x \le {{ - \pi } \over 2}} \cr {a\sin x + b} & ; & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x} & ; & {{\pi \over 2} \le x \le \pi } \cr } } \right.$$ and it is continuous on $$[-\pi, \pi]$$, then

A
$$a=1$$ and $$b=1$$
B
$$a=-1$$ and $$b=-1$$
C
$$a=-1$$ and $$b=1$$
D
$$a=1$$ and $$b=-1$$
4
COMEDK 2023 Morning Shift
+1
-0

The value of $$\lim _\limits{x \rightarrow \infty}\left(\frac{x^2-2 x+1}{x^2-4 x+2}\right)^{2 x}$$ is

A
$$e^2$$
B
$$e^4$$
C
$$e$$
D
$$e^{16}$$
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