piecewise function ... determine a and b so that f is differential at 0.
let f(x) = cosx , x> or equal to 0
ax+b, x<0
please help!!!
2006-10-02 05:43:49 · 3 answers · asked by streetspirit20 2 in Education & Reference ➔ Homework Help
i don't know if im' answering the right question. But to be differentiable at x=0, the function should be continuous at that point x=0. And only way to make these two function continuous is by making them meet at the same point when x=0.
and you know that at x=0, Cos x function is right at the point of y=1. So in order to do that the ax+b function should also be at 1 when x=0. And so the y intercept of that function should be 1.
so any funtion ax+ 1 will fulfill the condtion of continuous function. So b should be 1 but i think a can be any number. 2x=1, 3x+1, -4x+1, regardless of the a, it all meets at point y=1, and it will make a continuous funtion with Cos x at x=0.
2006-10-02 06:13:25 · answer #1 · answered by Anonymous · 0⤊ 0⤋
At x = 0, cos x = 1.
Thus, ax + b must = 1 at x = 0.
b = 1, a may be anything. (solution)
2006-10-02 13:10:58 · answer #2 · answered by ³√carthagebrujah 6 · 0⤊ 0⤋
I have NO idea, sorry..oh wait, maybe...
the cosx of x is obviously 55.67777 and if it is equal to 0 then the dividender cannot be 4 or more. so the way to figure this problem out is to coincide the answer with the effecient of x squared,
Does that help?
2006-10-02 12:51:13 · answer #3 · answered by marisol 2 · 1⤊ 2⤋