(i) Evaluate limx→1x+x2+x3+...+xn−nx−1
(ii) Find the derivative \sqrt{sin x} from first principle.
(i) n(n+12
(ii) cos x2√sin x
(i) Find the derivative of √(x−1)(x−2)(x−3)(x−4) + sin x1+tan x
(ii) Evaluate limx→0(1+x)6−1(1+x)2−1
If limx→1x+x2+x3⋯xn−nx−1=5050, then n equal
(i) If f(x)={x−|x|xif x≠02if x=0, show that limx→ 0 f(x) does not exist.
(ii) Evaluate limx→ 0 sin x−2 xin 3x+sin 5xx.
Or
(i) Find the derivative of (x−1)(x−2)(x−3)(x−4).
(ii) Differentiate xex by using first principle.
(i) Find the derivative of cosec x from the first principle.
(ii) Evaluate limx→√2x4−4x2+3√2x−8