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Test: Limits Of Rational Functions - JEE MCQ


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10 Questions MCQ Test - Test: Limits Of Rational Functions

Test: Limits Of Rational Functions for JEE 2024 is part of JEE preparation. The Test: Limits Of Rational Functions questions and answers have been prepared according to the JEE exam syllabus.The Test: Limits Of Rational Functions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Limits Of Rational Functions below.
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Test: Limits Of Rational Functions - Question 1
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The value of the limit  ​

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Test: Limits Of Rational Functions - Question 2
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The value of the limit 

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 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)

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Test: Limits Of Rational Functions - Question 3
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Test: Limits Of Rational Functions - Question 4
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What is the value of the limit ?
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Test: Limits Of Rational Functions - Question 5
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The value of the limit ​
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 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

Test: Limits Of Rational Functions - Question 6
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The value of the limit  
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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

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Test: Limits Of Rational Functions - Question 8
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The value of the limit

 
Test: Limits Of Rational Functions - Question 9
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Test: Limits Of Rational Functions - Question 10
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 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 

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