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

$$\lim _\limits{n \rightarrow \infty}\left(\frac{1}{1^5+n^5}+\frac{2^4}{2^5+n^5}+\frac{3^4}{3^5+n^5}+\ldots+\frac{n^4}{n^5+n^5}\right)=$$

A
$$\frac{1}{5} \log 3$$
B
$$\frac{1}{3} \log 5$$
C
$$\frac{1}{2} \log 5$$
D
$$\log \sqrt[5]{2}$$
2
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

$$\mathop {\lim }\limits_{n \to \infty } {{n{{(2n + 1)}^2}} \over {(n + 2)({n^2} + 3n - 1)}}$$ is equal to

A
0
B
4
C
2
D
$$\infty$$
3
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If the function $$f(x)$$, defined below, is continuous on the interval $$[0,8]$$, then $$f(x)=\left\{\begin{array}{cc}x^2+a x+b & , \quad 0 \leq x < 2 \\ 3 x+2, & 2 \leq x \leq 4 \\ 2 a x+5 b & , 4 < x \leq 8\end{array}\right.$$

A
$$a=3, b=-2$$
B
$$a=-3, b=2$$
C
$$a=-3, b=-2$$
D
$$a=3, b=2$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$f(x)$$, defined below, is continuous at $$x=4$$, then

$$f(x) = \left\{ {\matrix{ {{{x - 4} \over {|x - 4|}} + a} & , & {x < 4} \cr {a + b} & , & {x = 4} \cr {{{x - 4} \over {|x - 4|}} + b} & , & {x > 4} \cr } } \right.$$

A
$$a=0$$ and $$b=0$$
B
$$a=1$$ and $$b=1$$
C
$$a=-1$$ and $$b=1$$
D
$$a=1$$ and $$b=-1$$
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