JEE Exam  >  JEE Tests  >  Mathematics (Maths) for JEE Main & Advanced  >  Test: Infinite Limits - JEE MCQ

Test: Infinite Limits - JEE MCQ


Test Description

10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Infinite Limits

Test: Infinite Limits for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Infinite Limits questions and answers have been prepared according to the JEE exam syllabus.The Test: Infinite Limits MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Infinite Limits below.
Solutions of Test: Infinite Limits questions in English are available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Test: Infinite Limits solutions in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Infinite Limits | 10 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) for JEE Main & Advanced for JEE Exam | Download free PDF with solutions
1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Infinite Limits - Question 1

Detailed Solution for Test: Infinite Limits - Question 1

lim (x → 0) [((1-3x)+5x)/(1-3x)]1/x
lim (x → 0) [1 + 5x/(1-3x)]1/x
= elim(x → 0) (1 + 5x/(1-3x) - 1) * (1/x) 
= elim(x → 0) (5x/(1-3x)) * (1/x)
= elim(x → 0) (5x/(1-3x))
= e5

Test: Infinite Limits - Question 2

Detailed Solution for Test: Infinite Limits - Question 2

Test: Infinite Limits - Question 3

Detailed Solution for Test: Infinite Limits - Question 3

lim(x→0) [log10 + log1/10]/x
= [log10 + log10]/0
= 0/0 form
lim(x→0) [(1/(x+1/10) * 1]/1
lim(x→0) [(1/(0+1/10) * 1]/1
= 1/(1/10) => 10

Test: Infinite Limits - Question 4

Detailed Solution for Test: Infinite Limits - Question 4

Test: Infinite Limits - Question 5

Detailed Solution for Test: Infinite Limits - Question 5

lim(x → 1) (log2 2x)1/log2x
= lim(x →1) (log22 + log2x)1/log2x
As we know that {log ab = log a + log b}
lim(x → 1) {1 + log2x}1/log2x
log2x → 0
Put t = log2x
lim(t → 0) {1 + t}1/t
= e

Test: Infinite Limits - Question 6

Test: Infinite Limits - Question 7

lim(x → 0) (tanx/x)(1/x^2)

Detailed Solution for Test: Infinite Limits - Question 7

lim(x → 0) (tanx/x)(1/x^2)
= (1)∞
elim(x → 0) (1/x2)(tanx/x - 1)
= elim(x → 0) ((tanx - x)/x3)   .....(1)
lim(x → 0) ((tanx - x)/x3)
(0/0) form, Apply L hospital rule
lim(x → 0) [sec2x -1]/3x2
lim(x → 0) [tan2x/3x2]
= 1/3 lim(x → 0) [tan2x/x2]
= 1/3 * 1
= e1/3

Test: Infinite Limits - Question 8

Test: Infinite Limits - Question 9

Detailed Solution for Test: Infinite Limits - Question 9

lim(x → ∞) [(x-2)/(x+3)]2x
lim(x → ∞) [(x-2)/(x+3)]2 * [(x-2)/(x+3)]x


lim(x → a) [f(x) * g(x)] = lim(x → a) f(x) * lim(x → a) g(x)

lim(x → ∞) [(x-2)/(x+3)]2 * lim(x → ∞) [(x-2)/(x+3)]x
Lets evaluate the limits of both the functions separately,
lim(x → ∞) [(x-2)/(x+3)]2
= lim(x → ∞) [(x(1-2/x)/(1+3/x)]2
lim(x → ∞) [(1-2/x)/(1+3/x)]2
Apply infinity property,
= [(1-0)/(1-0)]2
= 1
Now, lim(x → ∞) [(x-2)/(x+3)]2
= lim(x → ∞) exln[(x-2)/(x+3)]
= lim(x → ∞) ln[(x-2)/(x+3)]/(1/x)
Apply L hospital rule
lim(x → ∞) d/dx[ln(x-2)/(x+3)]/[d/dx(1/x)]
= lim(x → ∞) {1/[(x-2)/(x+3)] * d/dx[(x-2)/(x+3)]}/(-1/x2)
= lim(x → ∞) {(x+3)/(x-2)[(x+3)d/dx(x-2) - (x-2)d/dx(x+3)]/(x+3)2}/(-1/x2)
= lim(x → ∞) {(x+3)/(x-2)[(x+3)-(x-2)]/(x+3)2}/(-1/x2)
= lim(x → ∞) {(x+3)/(x-2)[5/(x+3)2]}/(-1/x2)
= lim(x → ∞) [-5x2/(x+3)(x-2)]
= lim(x → ∞) [-5x2/(x2 + x - 6)]
Again apply L hospital rule,
= lim(x → ∞) [d/dx(-5x2)/(d/dx(x2 + x - 6))]
= lim(x → ∞) [-10x/(2x + 1)]
Again applying L hospital rule,
= lim(x → ∞) [d/dx(-10x)/(d/dx(2x + 1))]
=  lim(x → ∞) [-10/2] 
=  lim(x → ∞) [-5]
= -5
= lim(x → ∞) exln[(x-2)/(x+3)]2 = e(-5)2
= 1/e10
= lim(x → ∞) [(x-2)/(x+3)](x+3) = 1/e10 (1)
= 1/e10 = e-10

Test: Infinite Limits - Question 10

If a,b,c,d are positive, then 

209 videos|443 docs|143 tests
Information about Test: Infinite Limits Page
In this test you can find the Exam questions for Test: Infinite Limits solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Infinite Limits, EduRev gives you an ample number of Online tests for practice

Up next

Download as PDF

Up next

Download the FREE EduRev App
Track your progress, build streaks, highlight & save important lessons and more!