Prove that \(\frac { x }{ 1+x } \) < < log (1+ x) for x > 0.

Verify LMV theorem for f(x) = x³ - 2x² - x + 3 in [0, 1].

The volume of a cube is increasing at the rate of 8cm³/s.How fast is the surface area increasing when the length of an edge is 12cm?

Find the angle between two curves 2x²+y²=20 and x²-4y²+8=0

Write down the Taylor series expansion of the function cos x in ascending powers \(x-\frac { \pi }{ 4 } \) upto three non-zero terms.