1
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
2
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
3
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
4
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

If $$\lim _\limits{n \rightarrow \infty} x^n \log _e x=0$$, then $$\log _x 12=$$

A
negative
B
positive
C
zero
D
any value between $$-1$$ and 1
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