Question

h(t)=cot t, [pi/4,3pi/4] find the avg rate of change of the function over the given intervals HELP!!

Answer 1

Average rate of change is \[
\frac{h(t_2)-h(t_1)}{t_2-t_1}
\]

Answer 2

In this case \(t_1=\pi /4\) and \(t_2=3\pi/4\)

Answer 3

I understand that bit I don't get how you can plug the values in and get (-4/pi)

Answer 4

What is \(t_2-t_1\)?

Answer 5

pi/2?

Answer 6

Yep.
What is \(\cot(3\pi/4)-\cot(\pi/4)\)

Answer 7

cot(pi/2)

Answer 8

Nope!
You must evaluate \(\cot\) first!

Answer 9

What is \(\cot (3\pi/4)\)?

Answer 10

1.169422 or 1.17

Answer 11

No, \(\cot(3\pi/4)=-1\)

Answer 12

http://www.wolframalpha.com/input/?i=cot%283pi%2F4%29

Answer 13

And \(\cot(\pi/4)=1\)

Answer 14

Then simplify\[
\frac{-1-1}{\frac \pi 2}
\]

Answer 15

Okay I see how you got that now, I'm a little concerned though as to why my calculator gives me 1.69 for the \[\cot 3\pi \div4\]

Answer 16

im in radians

Answer 17

cot (3 x pi/4)

Answer 18

Never mind, I figured it out haha. Thanks for your help!!