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Maths-

General

Easy

Question

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus sin invisible function application x minus 1 over denominator x end fraction$

1
$e^{x}$
X
0

hint Hint:

In this question we will first use the L hospital theorem. Then we will put value of x.

The correct answer is: 0

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus sin invisible function application x minus 1 over denominator x end fraction$
using L hospital theorem,
$limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator d e to the power of x over denominator d x end fraction end style minus begin display style fraction numerator d sin x space minus 1 over denominator d x end fraction end style over denominator begin display style fraction numerator d x over denominator d x end fraction end style end fraction equals limit as x rightwards arrow 0 of fraction numerator e to the power of x minus cos space x over denominator 1 end fraction equals e to the power of 0 minus cos space 0 equals 1 minus 1 equals 0$

Related Questions to study

$blank to the power of n C subscript r plus 4 to the power of n C subscript r minus 1 end subscript plus 6 to the power of n C subscript r minus 2 end subscript plus 4 to the power of n C subscript r minus 3 end subscript plus to the power of n C subscript r minus 4 end subscript$ is equal to

$blank to the power of n C subscript r plus 4 to the power of n C subscript r minus 1 end subscript plus 6 to the power of n C subscript r minus 2 end subscript plus 4 to the power of n C subscript r minus 3 end subscript plus to the power of n C subscript r minus 4 end subscript$ is equal to

For the third resonance, which option shows correct mode shape for displacement variation and pressure variation.

For the third resonance, which option shows correct mode shape for displacement variation and pressure variation.

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$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator a to the power of x minus 1 over denominator b to the power of x minus 1 end fraction left parenthesis a greater than 0 comma b greater than 0 comma b not equal to 1 right parenthesis$

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$Lt subscript x not stretchy rightwards arrow 0 end subscript invisible function application fraction numerator e to the power of x minus 1 over denominator square root of 1 plus x end root minus 1 end fraction$

$Lt subscript x not stretchy rightwards arrow 0 end subscript invisible function application fraction numerator e to the power of x minus 1 over denominator square root of 1 plus x end root minus 1 end fraction$

If $a subscript n equals sum from r equals 0 to n of 1 over n subscript C subscript r end subscript text then end text sum from r equals 0 to n of fraction numerator r over denominator blank to the power of n C subscript r end fraction$ equal to

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$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$

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Match Column-I with Column-II and select the correct option from the codes given below.

Match Column-I with Column-II and select the correct option from the codes given below.

Some statements are given below each with one or two blanks. Select the option that correctly fills up the blanks.
i) High concentration of DDT disturbs _______ in birds, which causes _.
ii) burns more efficiently as compared to petrol and diesel.
iii) is the natural aging of a lake which occurs due to accumulation of __.
iv) _ reduces the number of organisms which are sensitive to high temperature.
v) Irreparable computers and other electronic goods are known as _____.

Some statements are given below each with one or two blanks. Select the option that correctly fills up the blanks.
i) High concentration of DDT disturbs _______ in birds, which causes _.
ii) burns more efficiently as compared to petrol and diesel.
iii) is the natural aging of a lake which occurs due to accumulation of __.
iv) _ reduces the number of organisms which are sensitive to high temperature.
v) Irreparable computers and other electronic goods are known as _____.

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