1
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $$f(x)=\left\{\begin{array}{cl}\frac{1}{|x|}, & \text { for }|x|>1 \\ a x^2+b, & \text { for }|x| \leq 1\end{array}\right.$$. If $$\lim _\limits{x \rightarrow 1^{+}} f(x)$$ and $$\lim _\limits{x \rightarrow 1^{-}} f(x)$$ exist, then the possible values for $$a$$ and $$b$$ are

A
$$a=b=1$$
B
$$a=-1 / 2, b=-3 / 2$$
C
$$a=3 / 2, b=-1 / 2$$
D
$$a=1 / 2, b=-3 / 2$$
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\frac{d}{d x}\left(\lim _{x \rightarrow 2} \frac{1}{y-2}\left(\frac{1}{x}-\frac{1}{x+y-2}\right)\right)=$$

A
$$1 / x^2$$
B
$$2 / x^3$$
C
$$-2 / x^3$$
D
$$1 / x^3$$
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=\left\{\begin{array}{cc}\frac{x^2 \log (\cos x)}{\log (1+x)} & , \quad x \neq 0 \\ 0 & , x=0\end{array}\right.$$, then at $$x=0, f(x)$$ is

A
not continuous
B
continuous but not differentiable
C
differentiable
D
not continuous, but differentiable
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $$f: R^{+} \longrightarrow R^{+}$$ be a function satisfying $$f(x)-x=\lambda$$ (constant), $$\forall x \in R^{+}$$ and $$f(x f(y))=f(x y)+x, \forall x, y, \in R^{+}$$. Then, $$\lim _\limits{x \rightarrow 0} \frac{(f(x))^{1 / 3}-1}{(f(x))^{1 / 2}-1}=$$

A
1/3
B
0
C
2/3
D
1
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