1
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $a, b, c$ and $k$ are non-zero real numbers and $\lim \limits_{x \rightarrow \infty} x\left(a^{1 / x}+b^{1 / x}+c^{1 / x}-3 k^{1 / x}\right)=0$, then $k=$
A
0
B
$(a b c)^{1 / 3}$
C
$(a b c)^{-1 / 3}$
D
1
2
TS EAMCET 2022 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim _{x \rightarrow 2} \frac{x^3-x^2-x-2}{2 x^3-3 x^2-3 x+2}= $$

A

0

B

$\infty$

C

$\frac{5}{7}$

D

$\frac{7}{9}$

3
TS EAMCET 2022 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim _{x \rightarrow 0} \frac{4[\sin (2022 x)-\sin (2020 x)]}{x[\cos (2022 x)+2 \cos (2021 x)+\cos (2020 x)]}= $$

A

1

B

2

C

2020

D

2021

4
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let [ $x$ ] denote the greatest integer less than or equal to $x$ and $f(x)=2 x-[2 x]$. If $\mathop {\lim }\limits_{x \to {2^ - }} f(x)=l_1$ and $\mathop {\lim }\limits_{x \to {2^ + }} f(x)=l_2$, then $l_1+l_2=$

A

1

B

2

C

0

D

4

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