EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET - 5 August 2021 Shift 1>Q 3

EASY

TS EAMCET

IMPORTANT

Earn 100

If $f (x) = \{\begin{matrix} \frac{\sin [x]}{[x]}, & [x] \neq 0 \\ 0, & [x] = 0 \end{matrix},$ where $[x]$ denotes the greatest integer less than or equal to $x,$ then $\lim_{x \to 0^{-}} f (x)$

50% studentsanswered this correctly

Important Questions on Limits

EASY

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET - 5 August 2021 Shift 1>Q 4

\lim_{x \to - \infty} \frac{3 | x |^{3} - x^{2} + 2 | x | - 5}{- 5 | x |^{3} + 3 x^{2} - 2 | x | + 7} =

EASY

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET - 5 August 2021 Shift 1>Q 5

If

f (x) = x^{2} \sin \frac{1}{x},

when

x \neq 0

and

f (0) = 0,

then

\lim_{x \to 0} f^{'} (x)

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET 2018 (04-May Shift-1)>Q 6

\lim_{x \to - \infty} \frac{3 |x| - x}{|x| - 2 x} - \lim_{x \to 0} \frac{\log (1 + x^{3})}{\sin^{3} x} =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET 2021 (04-Aug Shift-2)>Q 7

\lim_{x \to 0} \frac{(1 - \cos 2 x)}{x \tan 2 x + \frac{2 x}{3} \tan 3 x} =

EASY

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET 2021 (04-Aug Shift-1)>Q 8

\lim_{x \to 1} \frac{\log x}{(1 - x)} =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET 2021 (04-Aug Shift-2)>Q 9

\lim_{x \to 0} \frac{x^{2} 2^{x} - x^{2} \sin x - x^{2}}{3^{x} + \cos x - 3^{x} \cos x - 1} =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET 2021 (04-Aug Shift-2)>Q 10

If

\lim_{x \to 2} \frac{3 x^{2} - a x + 5 b}{x - 2} = 17

, then

a b =

HARD

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>TS EAMCET 2021 (04-Aug Shift-2)>Q 11

If

f (x) = \tan^{- 1} (\frac{\sqrt{1 + x} - \sqrt{1 - x}}{\sqrt{1 + x} + \sqrt{1 - x}})

, then

\lim_{_{x \to \frac{1}{2}}} \frac{2 [f (x) - f (\frac{1}{2})]}{2 x - 1} =