Find the value of?

Question

lim x^7 cos (9/x)
x->0
if the limit exists

Answer 1

Limit is zero.

0^7 = 0
And cos(oo) will be a value between -1 and 1. Times 0, 0.

Answer 2

Even B is right. The maximum value the cosine function can assume is 1 and its minimum is -1. So cos (9/x) would oscillate between those two values, while lim x ---> 0 of x^7 would increasingly approach 0 as a limit. The entire limit evaluates to max = 0 * (1) = 0 and min = 0 * (-1) = 0. Guess that leaves little room for any other value for the limit.

Answer 3

The limit is zero. The cosine is a bounded periodic function. and x^7 rapidly approaches zero.

Answer 4

limit is 0.