Question

Find an equation of the tangent line to the curve y=(e^x)(sinx) at the point (0,0).

Answer 1

1) find y'
2) find y' at (0,0). This is the slope
3) You have the slope, you have a point (0,0). You can form an equation by point-slope form

Answer 2

ok y'=e^xsinx+e^xcosx

Answer 3

when x=0 y=1

Answer 4

and when y=0 x=some random number

Answer 5

@Callisto

Answer 6

No....
You need to find the slope of tangent line at (0,0)
So, you need to sub (0,0) into y' to get the slope.

Answer 7

how do you plug a point into the equation. if you put in zero then that means you will get zero

Answer 8

Try.

Answer 9

Sorry, plug x=0 into y'

Answer 10

ok i did and got 1

Answer 11

1 is the slope m.
\[y-y_0 = m(x-x_0)\]\((x_0,y_0) = (0,0)\)

Answer 12

fyi, here is a graph

Answer 13

so the equation would be y=x

Answer 14

Yes.