Limit

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Question 1

What is the value of Limn→∞(1-1/n)2n ?
 

  • 1
     

  • e-2
     

  • e-1/2
     

  • 0
     

Question 2

[Tex]{\displaystyle \lim_{x \to \infty } \frac{x - \sin(x)}{x + \cos(x)}}[/Tex] equals

  • 1

  • -1

  • ∞

  • -∞

Question 3

Find the value of [Tex]\lim_{x\rightarrow 0}\frac{\tan x - x}{x^3}[/Tex]

  • 1/3

  • -1/6

  • 1/2

  • None of these

Question 4

[Tex]\lim_{x \to 4} \frac{\sin(x - 4)}{x-4} [/Tex]= ____.

Note: This question was asked as a Numerical Answer Type.

  • 0

  • 1

  • 2

  • 3

Question 5

What is the value of the limit: [Tex]\lim_{x \to 0} \frac{a^{mx}-b^{mx}}{\sin {(kx)}}[/Tex]

  • [Tex]\frac{1}{k} \ln \frac{a^m}{b^m}[/Tex]

  • [Tex]\frac{1}{k} \ln \frac{b^m}{a^m}[/Tex]

  • [Tex]\frac{2}{k} \ln \frac{a^m}{b^m}[/Tex]

  • [Tex]\frac{2}{k} \ln \frac{b^m}{a^m}[/Tex]

Question 6

Evaluate [Tex]\lim_{y\rightarrow 7}\frac{y^2-4y-21}{3y^2-17y-28}[/Tex].

  • 2/7

  • 3/5

  • 3/7

  • 2/5

Question 7

 

  • 1

  • -1

  • ∞

  • -∞

Question 8

The value of the following limit is [GATE CSE 2022]

 
  • -0.5

Question 9

Evaluate: 

 

  • 1/2

  • 2

  • 1/6

  • 0

Question 10

Evaluate:

 

  • 1/3

  • -1/2

  • -1/3

  • -1/4

Tags:
GATE CS

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