 Limits at Infinity homework Help at TutorEye

# Best Homework Help For Limits at Infinity

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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

Explanation: = Question 2: Evaluate (a) 1

(b) 0

(c) 2

(d) -1

Explanation: Question 3: Estimate (a) 1

(b) -1

(c) 0.5

(d) 0

Explanation: = {On dividing by x}

Question 4: Find the limit of (a) 1/2

(b) 0

(c) 1

(d) 1/4

Explanation:  Question 5: =

(a) 1

(b) 0

(c) (d) n

Explanation: All terms tends to 0

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

, g(x) ≥ f(x) > α

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

Explanation: Applying the L hospital’s rule

Question 8: is equal to

(a) 1

(b) e^2

(c) e

(d) 1/2

Explanation: = Question 9: is equal to

(a) 1

(b) 0

(c) -1

(d) -2

Explanation: Question 10: is equal to

(a) 1

(b) 0

(c) 1/2

(d) -1/2

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