Sketch f(x)=sin(x)/x
So far I found that the domain cannot equal 0. Thats its an even function because f(-x)=sin(-x)/(-x)=-sinx/-x, which gives you sin(x)/x. which is the same function. I have trouble finding out the vertical assymtotes but i think that there are none, and for horizontal assymtotes i got h.a=1 because of the ratio between the two highest values being 1. Then I found the first derivative which is f'(x)=(xcos(x)-sin(x))/x^2, and plugged in zero to get the maximum or minimum and got zero as the anwser. Im not sure where to go from here I know i need to find the second derivative, but I'm not completely sure if Im correct so far in my work. Help would be greatly appreciated.
Thank you.
So far I found that the domain cannot equal 0. Thats its an even function because f(-x)=sin(-x)/(-x)=-sinx/-x, which gives you sin(x)/x. which is the same function. I have trouble finding out the vertical assymtotes but i think that there are none, and for horizontal assymtotes i got h.a=1 because of the ratio between the two highest values being 1. Then I found the first derivative which is f'(x)=(xcos(x)-sin(x))/x^2, and plugged in zero to get the maximum or minimum and got zero as the anwser. Im not sure where to go from here I know i need to find the second derivative, but I'm not completely sure if Im correct so far in my work. Help would be greatly appreciated.
Thank you.
