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Limits at infinity:

 

When in a function the limit at x of f(x) is L, where L is finite if f(x) gets closer to L as x increases and becomes very large then we say that   f(x) = L (where L is a finite number).

And when limit of a function at x → - of f(x) is L, where L is finite if f(x) gets closer to L as x decreases x<0 and |x| is very large hence we say that  f(x) = L (where L is a finite number).

 

Limits at infinity Sample Questions:

Question 1: Find the limit of

 

(a) 1

(b) 2

(c) 0

(d) -1


Answer: (c)

Explanation:  = 

 

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Question 2: Evaluate

 

(a) 1

(b) 0

(c) 2

(d) -1


Answer: (b)

Explanation:

 

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Question 3: Estimate 

 

(a) 1

(b) -1

(c) 0.5

(d) 0


Answer: (c)

Explanation:  =  {On dividing by x}

 

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Question 4: Find the limit of

 

(a) 1/2

(b) 0

(c) 1

(d) 1/4


Answer: (d)

Explanation:

 

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Question 5:  =

 

(a) 1

(b) 0

(c) 

(d) n


Answer: (b)

Explanation: All terms tends to 0

 

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Question 6: Given that f(x) g(x) then which of the following is true

 


Answer: (a)

Explanation: (x) > 

, g(x) ≥ f(x) > α

 

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Question 7: If f(x) and g(x) be the functions such that f(a) = 0 and g(a) = 0 and f’(a)=0, g’(a) = 0 then =

 

(a)

(b)

(c) 

(d) None of these


Answer: (c)

Explanation: Applying the L hospital’s rule

 

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Question 8: is equal to

 

(a) 1

(b) e^2

(c) e

(d) 1/2


Answer: (c)

Explanation:  = 

 

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Question 9:  is equal to

 

(a) 1

(b) 0

(c) -1

(d) -2


Answer: (b)

Explanation:

 

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Question 10:  is equal to

 

(a) 1

(b) 0

(c) 1/2

(d) -1/2


Answer: (c)

Explanation: Let 1/x = y  =>  x = 1/yy 0

 

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