EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Continuity>MHT-CET 2019>Q 3

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MHT-CET

IMPORTANT

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If the function $f (x) = \{\begin{matrix} \frac{(e^{k x} - 1) \tan k x}{4 x^{2}}, & x \neq 0 \\ 16, & x = 0 \end{matrix}$ is continuous at $x = 0$ , then $k$ = ….

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Important Questions on Continuity

MEDIUM

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Continuity>MHT-CET 2019>Q 4

If function

f (x) = \{\begin{cases} x - \frac{|x|}{x}, x < 0 \\ 1, x = 0 \\ x + \frac{|x|}{x}, x > 0 \end{cases}

, then

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Continuity>MHT-CET 2018>Q 5

If

f (x) = x^{2} + α

for

x \geq 0 & f (x) = 2 \sqrt{x^{2} + 1} + β

for

x < 0

is continuous at

x = 0

and

f (\frac{1}{2}) = 2

then

α^{2} + β^{2}

is

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MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Continuity>MHT-CET 2018>Q 6

If

f (x) = \frac{e^{x^{2}} - \cos x}{x^{2}},

for

x \neq 0

is continuous at

x = 0

, then value of

f (0)

is

HARD

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Continuity>MHT-CET 2017>Q 7

If the function

f (x) = \{\begin{matrix} {[\tan (\frac{π}{4} + x)]}^{\frac{1}{x}} & f o r & x \neq 0 \\ k & f o r & x = 0 \end{matrix}

is continuous at

x = 0,

then

k = ?

EASY

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Continuity>MHT-CET 2017>Q 8

If

f (x) = \{\begin{matrix} \log {(\sec^{2} x)}^{\cot^{2} x} & f o r & x \neq 0 \\ K & f o r & x = 0 \end{matrix}

is continuous at

x = 0

then

K

is

MEDIUM

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Continuity>MHT-CET 2017>Q 9

If

f (x) = \{\begin{matrix} x & for & x \leq 0 \\ 0 & for & x > 0 \end{matrix}

then

f (x)

at

x = 0

is