1
AP EAPCET 2022 - 4th July Evening Shift
+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
$$1 / x^3$$
2
AP EAPCET 2022 - 4th July Evening Shift
+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
3
AP EAPCET 2022 - 4th July Morning Shift
+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
4
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

\begin{aligned} & \text { If } \lim _{x \rightarrow 0} \frac{|x|}{\sqrt{x^4+4 x^2+5}}=k \\ & \lim _{x \rightarrow 0} x^4 \sin \left(\frac{1}{3 \sqrt{x}}\right)=l \text {. Then, } k+l= \end{aligned}

A
0
B
1
C
$$-$$1
D
5
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