NIMCET 2018 Question Paper with solutions

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Question : 17 of 120

Marks: +1, -0

If

\lim↙{x→∞}

(1+a/x+b/x^2)^{2x}

=

e^2

, then the value of a and b are

a ∊ R , b = 2
a = 1 , b ∊ R
a ∊ R , b ∊ R
a = 1 , b = 2

Solution:

Given that,

\lim↙{x→∞}

(1+a/x+b/x^2)^{2x}

=

e^2

LHS is the form of

1{∞} ,

therefore

\lim↙{x→∞ } (1+1/x)^x

=

\lim↙{x→∞}

=

\lim↙{x→∞}

f (x)
Thus ,

\lim↙{x→∞}

(a/x+b/x^2)^{2x}

=

e^2

using property
⇒

\lim↙{x→∞} (2a+{2b}/x)

=

e^2

⇒

2^(2a+0)

=

e^2

On comparing exponent power both sides, we get
a = 1 , b ∊ R

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