Find the points of x the curve y = x³ − 3x² + x − 2 at which the tangent is parallel to the line y = x 

Find the equation of the tangent and normal to the Lissajous curve given by x = 2cos 3t and y = 3sin 2t, t ∈ R

Expand log(1+ x) as a Maclaurin’s series upto 4 non-zero terms for –1 < x ≤ 1.

Expand tan x in ascending powers of x upto 5^th power for \(-\frac{\pi}{2} <x<\frac{\pi}{2}\)

Find the intervals of monotonicity and hence find the local extrema for the function f(x) = x² − 4x + 4

Find the intervals of monotonicity and hence find the local extrema for the function \(f(x)=x^{\frac{2}{3}}\).

Discuss the monotonicity and local extrema of the function \(f(x)=log(1+x)-\frac{x}{1+x},x>-1\) and hence find the domain where, \(log(1+x)>\frac{x}{1+x}\)

Find the intervals of monotonicity and local extrema of the function f(x) = x log x + 3x.

Prove that among all the rectangles of the given area square has the least perimeter.

Find the points on the unit circle x² + y² = 1 nearest and farthest from (1, 1).