1
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

$$\lim _\limits{z \rightarrow 1} \frac{z^{(1 / 3)}-1}{z^{(1 / 6)}-1}$$ is equal to

A
$$-$$1
B
1
C
2
D
$$-$$2
2
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

$$f(x)=\left\{\begin{array}{cc} \frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}, & x \neq 0 \\ K \log 2 \log 3, & x=0 \end{array}\right.$$

Find the value of $$k$$ for which the function $$f$$ is continuous.

A
$$\sqrt{2}$$
B
$$24$$
C
$$18 \sqrt{3}$$
D
$$24 \sqrt{2}$$
3
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

If the function $$f(x)$$, defined below is continuous in the interval $$[0, \pi]$$, then $$f(x)=\left\{\begin{array}{cc}x+a \sqrt{2}(\sin x) & , \quad 0 \leq x < \frac{\pi}{4} \\ 2 x(\cot x)+b, & \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ a(\cos 2 x)-b(\sin x), & \frac{\pi}{2} < x \leq \pi\end{array}\right.$$

A
$$a=\frac{\pi}{6}, b=\frac{\pi}{12}$$
B
$$a=\frac{-\pi}{6}, b=\frac{\pi}{12}$$
C
$$a=\frac{-\pi}{6}, b=\frac{-\pi}{12}$$
D
$$a=\frac{\pi}{6}, b=\frac{-\pi}{12}$$
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