For 0<x1, (1+x)/x=1+bx+cx2+. Find b and c, respectively.

GATE 2023 PI – Question 13

Engineering Mathematics · Calculus · 1 mark · Multiple choice

For $0<x\le1$, $\ln(1+x)/x=1+bx+cx^2+\cdots$. Find b and c, respectively.

Show answer and explanation

Correct answer: (A) −1/2 and 1/3

Expand $\ln(1+x)=x-x^2/2+x^3/3-\cdots$ and divide by x. Comparing coefficients gives **b = −1/2, c = 1/3, A**.

GATE 2023 PI Q36 – z(x,y)=ex-2y, x(t)=et, y(t)=e-t, with all variables real. Find dz/dt.
GATE 2022 PI Q45 – Evaluate x1(x3-3x+2)/(x3-x2-x+1) to one decimal.
GATE 2021 PI Q35 – Find the minimum of f(x,y,z)=x2+5y2+5z2-4x+40y-40z+300 (integer).
GATE 2026 PI Q34 – Evaluate C(2x\,dx+2y\,dy+2z\,dz), where C is a semicircle in z = 0 starting at (0,0,0) and…
GATE 2025 PI Q12 – For orthogonal Cartesian unit vectors i,j,k, find the curl of -2y i+x j.
GATE 2025 PI Q37 – Which function is analytic in z = x + iy, with i=-1?