100th Derivative

Calculus Level 2

Evaluate the 100th derivate of the given function at x=0.

-8 -1 8 0

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Let, y = f ( x ) = 4 x 3 8 cos x y = f(x) = 4x^{3} - 8\cos x

Let y n y_n be the n t h n_{th} derivative.

It is clear that. 10 0 t h 100_{th} derivative of. 4 x 3 4x^{3} will be zero.

8 cos x -8\cos x follows a pattern in its derivatives. 8 sin x , 8 cos x , 8 sin x , 8 cos x , . . . . . . . . 8\sin x , 8\cos x , -8\sin x , -8\cos x , ........ After every 4 derivatives it repaeats.

100 4 = 25 \dfrac {100}{4} = 25 .Hence, after 25 cycles its repeats to the same, i.e, y 100 = 8 cos x = 8 y_{100} = -8\cos x = -8 .Since, x = 0. x = 0.

A N S W E R : 8 ANSWER :\boxed{-8}

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...