1
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim _{x \rightarrow 0} \frac{\left(3^{2 x}-\sqrt{x+1}\right) \sin 5 x}{1-\cos 4 x}= $$

A

$\frac{3}{5}(\log 18-1)$

B

$\frac{5}{16} \log \left(\frac{81}{e}\right)$

C

$\frac{4}{15}(\log 81-1)$

D

$\frac{16}{5}[\log (27)-1]$

2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim\limits_{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right)= $$

A
$\pi / 2$
B
$2 / \pi$
C
1
D
0
3
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(9)=9$ and $f^{\prime}(9)=4$, then $\lim\limits_{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}=$

A
3
B
4
C
6
D
9
4
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \lim \limits_{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}= $$
A
$\frac{1}{10}$
B
$-\frac{1}{10}$
C
$\frac{2}{5}$
D
$-\frac{2}{5}$

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