1
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=\left\{\begin{array}{cc}\frac{e^{\alpha x}-e^x-x}{x^2}, & x \neq 0 \\ \frac{3}{2}, & x=0\end{array}\right.$$

Find the value of $$\alpha$$ for which the function $$f$$ is continuous

A
1
B
0
C
4
D
2
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

The value of $$k(k > 0)$$, for which the function $$f(x)=\frac{\left(e^x-1\right)^4}{\sin \left(\frac{x^2}{k^2}\right) \log \left(1+\frac{x^2}{2}\right)}$$, where $$x \neq 0$$ and $$f(0)=8$$

A
1
B
4
C
2
D
3
3
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$f^{\prime \prime}(x)$$ is continuous at $$x=0$$ and $$f^{\prime \prime}(0)=4$$, then find the following value. $$\lim _\limits{x \rightarrow 0} \frac{2 f(x)-3 f(2 x)+f(4 x)}{x^2}$$ is equal to

A
4
B
8
C
12
D
16
4
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+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
AP EAPCET Subjects
EXAM MAP