Thread: Continuity lim x->-13*pi/14 cos(7x - cox(7x))

1. Originally Posted by Subhotosh Khan
Hint:

cos(π/2) = 0
cos(pi/2)=0

see my answer in previous post. does my work look correct? answer is 1?

2. Originally Posted by muzik
cos(pi/2)=0

see my answer in previous post. does my work look correct? answer is 1?
When you plugged this into your calculator (in "radian" mode), what did you get? You plugged $-\frac{13}{14}\pi$ in for "x" in the inner cosine:

. . . . .$7\, \left(-\dfrac{13}{14}\pi\right)\, =\, -\dfrac{13}{2}\pi$

. . . . .$-\dfrac{13}{2}\pi\, =\, -\dfrac{16}{2}\pi\, +\, \dfrac{3}{2}\pi\, =\, -8\pi\, +\, \dfrac{3}{2}\pi$

. . . . .$\cos\left(-\dfrac{13}{2}\pi \right)\, =\, \cos\left(\dfrac{3}{2}\pi \right)\, =\, ...?$

You plugged this result into the argument for the outer cosine, and got... what? Then you evaluated the outer cosine at this value and got... what? How did you arrive at "1"?

3. Originally Posted by stapel
When you plugged this into your calculator (in "radian" mode), what did you get? You plugged $-\frac{13}{14}\pi$ in for "x" in the inner cosine:

. . . . .$7\, \left(-\dfrac{13}{14}\pi\right)\, =\, -\dfrac{13}{2}\pi$

. . . . .$-\dfrac{13}{2}\pi\, =\, -\dfrac{16}{2}\pi\, +\, \dfrac{3}{2}\pi\, =\, -8\pi\, +\, \dfrac{3}{2}\pi$

. . . . .$\cos\left(-\dfrac{13}{2}\pi \right)\, =\, \cos\left(\dfrac{3}{2}\pi \right)\, =\, ...?$

You plugged this result into the argument for the outer cosine, and got... what? Then you evaluated the outer cosine at this value and got... what? How did you arrive at "1"?

so..
=cos((3pi/2)-cos(3pi/2)) correct?
=cos((3pi/2)-0)
=cos(3pi/2)
=0

I got 1 because my algebra needs a lot of help. Thanks for you help.

4. Originally Posted by muzik
cos(pi/2)=0

see my answer in previous post. does my work look correct? answer is 1?
Thanks for you help. i know understand. took me awhile.

5. Originally Posted by Dr.Peterson
I take back what I said! Do the simplification correctly, and evaluate by hand as far as you can. What is the value of the cosine of -13*pi/2? Think about it!
Thank you for your help. I now understand the problem and got the answer correct. i was going to input 1 but waited like you said proof read before submit. I wasn't sure on 1 as the answer so i waited till i was sure.

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