Question

Find the intersection point of the two curves below:
y = 4sinx
y = e^{4x}

Answer 1

Can this be done algebraically?

Answer 2

solve \(4 \sin x=e^{4x}\)

Answer 3

How?

Answer 4

How can you get the x-term by itself?

Answer 5

so is that 2 graphs y=sinx AND y = e^4x?

Answer 6

Yes

Answer 7

4sinx = e^(4x)

Answer 8

Yea

Answer 9

o wth that looks confusing

Answer 10

How you tried graphing the two functions to see where they cross?

Answer 11

Ok lets say I am not allowed to use a graphing calculator.

Answer 12

ok lets take ln on both sides to get ln(4sinx) = 4x on the left side we can right ln 4 + ln(sinx) = 4x

Answer 13

The you can use pencil and paper which is much better anyway.

Answer 14

I really doubt there is an analytic way to do this
best using some approximation technique like newton-ralphson or somethin

Answer 15

@markriggs Yes, but that requires me to get the intersection points. I have to find the area of the region b/ween y = 4sinx and y =e^{4x} bounded by x = 0 and x = pi/2. That is the full question

Answer 16

And for me to do that, I need to find the intersection points in the MIDST of these boundaries

Answer 17

The two functions do not cross on the interval (0,pi/2).

Answer 18

Really?

Answer 19

really

Answer 20

No I am pretty sure they do

Answer 21

sinx starts at 0
e^(4x) starts at 1 and grows faster
they do not intersect in that interval

Answer 22

Wow

Answer 23

markriggs, that was great. I was completely doubting that because I never really ended up with a situation like that

Answer 24

Ok I think that is about it. I can work out the area. Next time I will check to make sure with graphing software if they ever intersect

Answer 25

Sin(0)=0 e^(4*0)=1

Sin(pi/2)=1 e^2Pi=535

You really should draw a picture first..

Answer 26

No I did. But I drew it incorrectly.

Answer 27

Ok thanks all