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

[muzik]

Help please
I should be able to just apply x into the function but I'm having trouble solving

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

I get to

cos(-13*pi/2 - cos(-13*pi/2))

what next?

Thanks

 

[stapel]

I should be able to just apply x into the function but I'm having trouble solving

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

Would it be correct to interpret the above as follows?

. . . . .$\displaystyle \displaystyle \lim_{x \rightarrow -\frac{13\pi}{14}}\, \cos\left(7x\, -\, \cos(7x)\right)$

I get to

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

what next?

Is there any reason you can't just plug-n-chug in your calculator?

 

[Dr.Peterson]

Help please
I should be able to just apply x into the function but I'm having trouble solving

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

I get to

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

Yes, since the cosine is continuous (and I assume you meant cos everywhere, not cox), you just have to find the value of cos(7x - cos(7x)) when x = -13*pi/14. But that is not what you did. Is that just more typos, or is the problem something other than what you wrote? You don't seem to have multiplied by 7 in either place. You should have

cos(7(-13*pi/14) - cos(7(-13*pi/14)))

Once you do the right substitution, just use a calculator to do what you wrote!

 

[muzik]

Thanks for the replies and sorry for the typos
Stapel, Yes that's correct interpretation.

ok if I enter into calculator I get 0.8414.

It's my last attempt on the answer for the problem. Does 0.8414 sound right?
The requirement is to "Simplify your answer" Usually it will say up to 4 decimal places.

 

[muzik]

Yes, since the cosine is continuous (and I assume you meant cos everywhere, not cox), you just have to find the value of cos(7x - cos(7x)) when x = -13*pi/14. But that is not what you did. Is that just more typos, or is the problem something other than what you wrote? You don't seem to have multiplied by 7 in either place. You should have

cos(7(-13*pi/14) - cos(7(-13*pi/14)))

Once you do the right substitution, just use a calculator to do what you wrote!

I was trying to simplify. The 7 with the denominator 14. so with out the cosine I was trying to simplify 7(-13*pi/14) so I that's how I got -13*pi/2. oops and I wrote -13*pi/7 in my earlier post.

I'm just thinking the answer is not in decimal form.

Thanks for your help.

 

[Dr.Peterson]

I was trying to simplify. The 7 with the denominator 14. so with out the cosine I was trying to simplify 7(-13*pi/14) so I that's how I got -13*pi/2. oops and I wrote -13*pi/7 in my earlier post.

I'm just thinking the answer is not in decimal form.

I would expect the answer to be a decimal - trig functions are rarely rational.

What answer do you get? Show us that, and the specific calculation you really do to get it.

And, as you've learned, be sure to proofread before you hit Submit!

 

[Dr.Peterson]

I would expect the answer to be a decimal - trig functions are rarely rational.

What answer do you get? Show us that, and the specific calculation you really do to get it.

And, as you've learned, be sure to proofread before you hit Submit!

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!

 

[muzik]

So i'm down to

cos((-pi/2)-cos(-pi/2)) correct?
=cos((-pi/2)-0)
=cos(0-0)
=cos (0)
=1

 

[muzik]

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!

cos(-pi/2) ?

 

[Deleted member 4993]

cos(-pi/2) ?

Hint:

cos(π/2) = 0

 

[muzik]

Hint:

cos(π/2) = 0

cos(pi/2)=0

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

 

[stapel]

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 $\displaystyle -\frac{13}{14}\pi$ in for "x" in the inner cosine:

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

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

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

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"?

Please be complete. Thank you!

 

[muzik]

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

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

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

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

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"?

Please be complete. Thank you!

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.
​

 

[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.

 

[muzik]

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.