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Grade 11 Exam  >  Grade 11 Tests  >  Test: Logarithmic And Exponential Limits - Grade 11 MCQ

Test: Logarithmic And Exponential Limits - Grade 11 MCQ


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10 Questions MCQ Test - Test: Logarithmic And Exponential Limits

Test: Logarithmic And Exponential Limits for Grade 11 2025 is part of Grade 11 preparation. The Test: Logarithmic And Exponential Limits questions and answers have been prepared according to the Grade 11 exam syllabus.The Test: Logarithmic And Exponential Limits MCQs are made for Grade 11 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Logarithmic And Exponential Limits below.
Solutions of Test: Logarithmic And Exponential Limits questions in English are available as part of our course for Grade 11 & Test: Logarithmic And Exponential Limits solutions in Hindi for Grade 11 course. Download more important topics, notes, lectures and mock test series for Grade 11 Exam by signing up for free. Attempt Test: Logarithmic And Exponential Limits | 10 questions in 10 minutes | Mock test for Grade 11 preparation | Free important questions MCQ to study for Grade 11 Exam | Download free PDF with solutions
Test: Logarithmic And Exponential Limits - Question 1
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Detailed Solution for Test: Logarithmic And Exponential Limits - Question 1

lim(x → 0) (ex + e-x - 2)/x2
it is (0/0) form, hence apply L hospital rule
Taking derivative, we get
lim(x → 0) (ex - e-x)/2x
lim(x → 0) (ex + e-x)/2
= (1 + 1)/2 
⇒ 2/2 = 1

Test: Logarithmic And Exponential Limits - Question 2
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Detailed Solution for Test: Logarithmic And Exponential Limits - Question 2

 lim(x → 0) log(1+x)/[√(1+x)-1)]
= lim(x → 0) log(1+x)/[√(1+x)-1)] * {[√(1+x)+1) * [√(1+x)+1)]}
= lim(x → 0) [log(1+x)/x] * (√(1+x)+1)
= 1 * (2)
= 2

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Test: Logarithmic And Exponential Limits - Question 3
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Test: Logarithmic And Exponential Limits - Question 4
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Test: Logarithmic And Exponential Limits - Question 5
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Test: Logarithmic And Exponential Limits - Question 6
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Detailed Solution for Test: Logarithmic And Exponential Limits - Question 6

lim(x → 0) (x2x - x)/(1-cosx)
lim(x → 0) x2(2x - 1)/x(1-cosx)
By formula : lim(x → 0) (ax - 1)/x = log a
lim(x → 0) x2 log2/(1-cosx)
Differentiate it 
lim(x → 0) 2x log2/(sinx)
= 2 log2

Test: Logarithmic And Exponential Limits - Question 7
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Detailed Solution for Test: Logarithmic And Exponential Limits - Question 7


 

Test: Logarithmic And Exponential Limits - Question 8
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 is equal to
Detailed Solution for Test: Logarithmic And Exponential Limits - Question 8


⇒ Using L'Hospital,

= 1/2

Test: Logarithmic And Exponential Limits - Question 9
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Find log5125
Detailed Solution for Test: Logarithmic And Exponential Limits - Question 9

53 = 125 
As we know, 
ab = c ⇒ logac = b 
Therefore; Log5125 = 3

Test: Logarithmic And Exponential Limits - Question 10
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Solve the following
Detailed Solution for Test: Logarithmic And Exponential Limits - Question 10

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