Question

please answer the question in math​

Answer 1

Answer:

f(0) = lim. 1 - cos(1 - cosx) /x^4

x->0

applied Leibniz rule...

f(0) = lim x->0. (sin(1-cosx) * sinx) / 4x³

we know that limx->0 sinx/x = 1 put in equantion

f(0) = lim x->0 (sin(1-cosx))/ 4x²

furthur applied Leibniz

f(0) = lim x->0 (cos(1-cosx)* (sinx)) / 8x

f(0) = lim x-> 0 ( cos(1-cosx) )/ 8

now put limit x -> 0

we get

f(0) = cos(0)/8

= 1/8