GATE 2022 ES – Question 34

Mathematics Foundation · Calculus · 1 mark · Numerical answer

Find $\lim_{x\to0}(\sqrt{1+x}-1)/x$, to one decimal.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.5 to 0.5

Explanation

Rationalize the numerator to get $1/(\sqrt{1+x}+1)$ for x≠0. Its continuous limit at zero is 1/(1+1)=**.5**. Direct substitution initially gives 0/0, so cancelling through the conjugate is necessary.

More Calculus questions

GATE 2022 ES Q36 – For y+4y=0, y(0)=0 and y(0)=1, identify problem and solution.
GATE 2022 ES Q52 – Find area enclosed by y=x, y=3x and x=0,x=1, to one decimal.
GATE 2021 ES Q11 – Find slope of the tangent to y=x² at(x, y)=(3,9).
GATE 2021 ES Q12 – Evaluate x0x2/ x.
GATE 2021 ES Q30 – For dependent y and independent x, classify dy/dx=x2y.
GATE 2021 ES Q31 – Which listed values solve x3-10x2+31x-30=0?

All Calculus questions →