Consider the following expression. _x -3 2x + 22 - 4x + 3 The value of the above expression (rounded to 2 decimal places) is ________.

GATE CSE 2021 Set 1 Q30: Limit of (√(2x+22) − 4)/(x+3) as x → −3

Consider the following expression.

$\lim_{x \to -3} \frac{\sqrt{2x + 22} - 4}{x + 3}$

The value of the above expression (rounded to 2 decimal places) is ________.

Try it: numerical answer: type the value

Your answer

Numerical answer. No negative marking.

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Answer: 0.25 (official GATE 2021 final answer key)

Concept used: A $0/0$ form: rationalise the numerator or use L'Hôpital's rule.

First step: Differentiate top and bottom: $\frac{d}{dx}\sqrt{2x+22} = \frac{1}{\sqrt{2x+22}}$ , evaluated at $x = -3$ .

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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key