Question

What is the limit as x approaches zero of sin(ax)/bx?

Answer 1

HI!!

Answer 2

make a guess i bet you will be right

Answer 3

I was thinking 1

Answer 4

@misty1212

Answer 5

oh no
if it was
\[\frac{\sin(x)}{x}\] then it would be 1

Answer 6

but it is
\[\frac{\sin(ax)}{bx}\]

Answer 7

you want a method? it is kind of silly

Answer 8

I am using the l'hopitals rule

Answer 9

oh hell no

Answer 10

like killing a fly with a 45

Answer 11

\[\frac{\sin(ax)}{bx}=\frac{\sin(ax)}{ax}\times \frac{a}{b}\]

Answer 12

I dont understand

Answer 13

that is just some silly algebra to show you that it is \(\frac{a}{b}\) since
\[\lim_{x\to 0}\frac{\sin(x)}{x}=1\]

Answer 14

i will bet to a/b

Answer 15

so you get \[1\times \frac{a}{b}\]

Answer 16

well seems you already solved this hehe

Answer 17

you can use l'hopital too but it is dumb
\[\frac{a\cos(ax)}{b}\]

Answer 18

so then it would be a/b?

Answer 19

\[\color\magenta\heartsuit\]

Answer 20

okay thank you!

Answer 21

yw