Test: Limits Of Rational Functions


10 Questions MCQ Test Mathematics For JEE | Test: Limits Of Rational Functions


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QUESTION: 1

The value of the limit  ​

Solution:

QUESTION: 2

The value of the limit 

Solution:

 lim (x2-9)/x3+9x-6x2
Lim x=0
lim[(0)2 - 9]/ (0)3 + 9(0) - 6(0)2
-9/0 (which is not defined)

QUESTION: 3

Solution:

QUESTION: 4

Solution:

 √x+1−1 / x

=(√x+1−1)(√x+1+1) / x(√x+1+1)

=x+1−1 / x(√x+1+1) 

= 1/√x+1+1

 So  limx→0 √x+1−1/x

≡ limx→0  1/√(x+1)+1

     = ½

QUESTION: 5

The value of the limit 

Solution:

 lt x->-2 (1/x + 1/2) / x+2
lt x->-2 (2+x)/2x(x+2)
lt x->-2 (1/2x)
= 1/2(-2) = -¼

QUESTION: 6

The value of the limit  

Solution:

lim x → 2 [(2x - 4) (2x - 2) ((√2x) + 2)]/[(√2x - 2) (√2x - 2)]
= lim x → 2 [(2x - 4) (2 *4)]/(√2x - 2)
= 2 lim(x → 2) [(√2x)2 - (2)2]/(√2x - 2)
= 2 lim(x → 2) [(√2x)2 + 2) (√2x)2 - 2)]/(√2x - 2)
= 8

QUESTION: 7

Solution:

QUESTION: 8

The value of the limit

 

Solution:
QUESTION: 9

Solution:

QUESTION: 10

Solution:

 limx→1x9−1/x5−1 has indeterminate initial form (it has form 0/0). Therefore 1is a zero and x−1 a factor of both the numerator and the denominator.
limx→1 x10−1/x5−1
= limx→1[(x−1)(x8+x7+x4….⋅+x+1)]/(x−1)(x5+x6+x4+⋅⋅⋅+x+1)
= (1+1+1+1+.....upto 10 terms)/(1+1+1+⋅⋅⋅upto 5 terms)
= 10/5 = 2