Question

Find a value of k making h(x) continuous on [0,5].
**functions attached inside**
k=_______

Answer 1

:)

Answer 2

so would you start off like this?

e^kx = x + 3

?

Answer 3

lim f(x) = lim f(x)
x->2-....x->2+

Answer 4

As before, you look for the x value at which one part of the function gives way to the other part. This happens at x=2.

Hey! You're doing great. You've written e^kx = x + 3 . Let x = 2 and solve the resulting equation for k.

There are various ways of doing this. I got k = (ln 5)/2 (which is NOT the only way in which you could write the correct answer).

sorry, I've been on Open Study 12 hours or more today; time for me to his the sack. Come back later this week (or even tomorrow).

Answer 5

okay :) wow haha no worries :) rest up!

Answer 6

Plugin the value of x at the boundary.

Answer 7

so e^k(2) = 2+3

so e^2k = 5

? what do i do from here?

Answer 8

take ln of both sides

Answer 9

lne^2k = ln5

?

Answer 10

And lne = ...?

Answer 11

1 ?

Answer 12

So this lne^2k = ln5 becomes...

Answer 13

remember lne^2k = 2k*lne

Answer 14

ahh okay..

so 2k(1)=ln5
2k=ln5
k=ln5/2 ?

Answer 15

ahh okay..

so 2k(1)=ln5
2k=ln5
k=ln5/2 ?

Answer 16

Yep.

Answer 17

awesome! :) thanks!!

Answer 18

awesome! :) thanks!!