Question

time for a random fun calculus problem

Answer 1

POST AWAY!

Answer 2

fun calculus...oxymoron?

Answer 3

im weak with Calculus >.<

Answer 4

upside down

Answer 5

no its upside down lol

Answer 6

time for an upside down cal problem lol

Answer 7

fun calc problem? that is random

Answer 8

medal 2 the 1st to solve it! or the funniest post...

Answer 9

i wanted to do the question with that circl involved

Answer 10

I saw a newtwon method and I walk away

Answer 11

let me stand on my head. i'll be back in an hour

Answer 12

let me type the question k?

Answer 13

ilke newton's method

Answer 14

but then someone named leibniz probably wouldn't want much to do with someone named newton

Answer 15

dere. you all cool now.

Answer 16

The circle has radius OA equal to 1, and AB is tangent to the the circle at A. The arc AC has radian measure theta and the segment AB also has length theta. The line through B and C crosses the x-axis at P(x,0)
the questions are...

Answer 17

Im holding my Laptop upside down to read it.

Answer 18

u are sooo clever khan

Answer 19

Haha.

Answer 20

:)

Answer 21

(a) Show that the length if PA is
\[1-x=\frac{\theta*(1-\cos(\theta))}{\theta-\sin(\theta)}\]

Answer 22

i will try to make a better copy of this scan i dont think i will be able to copy it upside correctly

Answer 23

of not if*

Answer 24

Rotate the picture, lol

Answer 25

i stole your book <.<

Answer 26

you have my book or did you take my picture?

Answer 27

its all blurry! Not that I could solve it anyways...

Answer 28

i just cropped your picture and rotated it lol

Answer 29

LOL just use stduviewer and rotate pages..

Answer 30

lol

Answer 31

we should talk to the people in the computers study group

Answer 32

(b) andfind
\[\lim_{\theta \rightarrow 0}(1-x)\]

(c) Show that \[\lim_{\theta \rightarrow \infty}[(1-x)-(1-\cos(\theta)]=0\]

Answer 33

there is a roach on my desk
i cant stay here
they freak me out

Answer 34

ok my cat got it

Answer 35

i will do these problems while watching rescue me
and we can compare answers later :) if anyone is interested in doing the questions

Answer 36

good for u. My dog's currently dreaming either of eating or throwing up;can't tell which

Answer 37

lol

Answer 38

This is geometry, I don't understand geometry, plus My name is Earl is on

Answer 39

got a, posting solution in a sec.

Answer 40

it is also easy to find the equation of the line that passes through C and B and then find the root. that gives you P

Answer 41

Slope of the line between connecting C and B is

\[\frac{\theta-\sin(\theta)}{1-\cos(\theta)}\]

equation of line is

\[y-\theta=\frac{\theta-\sin(\theta)}{1-\cos(\theta)}(x-1)\]

let y=0

solve for 1-x

Answer 42

very nice :) for b im getting 3 <.<
posting that in a sec as well. had to use L'Hopital's Rule a couple of times.

Answer 43

For c), just play with the expression till you end up with a theta term in the denominator only. Since all the sin and cos terms are bounded between -1 and 1, the theta term in the denominator will ultimately drive the lim to 0.

Answer 44

Can anyone do (b) without using L'Hopitals rule :)

Answer 45

joe i thought u said you weren't good at calculus

Answer 46

very good you guys

Answer 47

i think i got b) without l'hopital, but it is not in any way simpler than l'hopital since i use power series expansion of numerator and denominator.
wondering what the snap way is if there is one

Answer 48

L'Hospitals rule is definitely the easiest way to do it (not counting using a computer/calculator).

I use the Taylor expansion of sine and the fact that

\[\lim_{x\to 0}\frac{\sin(x)}{x}=1\]to find the limit.