GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

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Question : 31 of 65

Marks: +1, -0

The value of

\lim ↙{x → ∞} \;{√{9 x^{2}+2020}}/{x+7}

is

3
indeterminable
$\;{7}/{9}$
1

Solution:

\lim ↙{x → ∞} \;{√{9 x^{2}+2020}}/{x+7}

Dividing numerator and denominator by '

x^{'}

\lim ↙{x → ∞} \;{\;{√{9 x^{2}+2020}}/{x}}/{{x+7}/{x}}

\lim ↙{x → ∞} \;{√{{9 x^{2}}/{x^{2}}+{2020}/{x^{2}}}}/{1+\;{7}/{x}}

\lim ↙{x → ∞} \;{√{{9+2020}/{x^{2}}}}/{1+\;{7}/{x}}

Putting

x → ∞ ⇒ \;{1}/{x^{2}} → 0, \;{1}/{x} → 0

=\;{√{9+0}}/{1+0}=\;{√{9}}/{1}=3

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