Calculus HELP!!!!

[ladyofvirtue91]

I need to graph the function 2 cos x + x, x ∈ [0,2π]
I know how to graph but I need help finding the domain, range, x and y intercepts, and asymptotes (vertical, horizontal, slanted). Thanks in advance for any help you can give. Please show the steps if you can so I can understand. I know how to find the derivatives already. But not sure how to find the others.

 

[Deleted member 4993]

I need to graph the function 2 cos x + x, x ∈ [0,2π]
I know how to graph but I need help finding the domain, range, x and y intercepts, and asymptotes (vertical, horizontal, slanted). Thanks in advance for any help you can give. Please show the steps if you can so I can understand. I know how to find the derivatives already. But not sure how to find the others.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

It seems that you have problem with the beginig of the problem. So:

Please define domain of a function for us.

Please define x and y intercepts of a function for us.

Please define asymptotes (vertical, horizontal, slanted) of a function for us.

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[ladyofvirtue91]

Sorry, I wasn't aware. I'm new here and just needed quick help.

I know domain, x and y intercepts, and asymptotes when it comes to regular functions that don't involve sine, cosine, etc

Domain can be defined as the values that x can be and for range you answer the question what can y or in this case f(x) be.
x and y intercepts is when you set x and y = 0 respectively.
This is where I'm stuck.
I'm thrown off because it's a trig function
when x = 0 f(x) = 2
but when y or f(x) = 0 I don't know how to find x? Do I factor or what?

For the asymptotes
to find the vertical asymptotes you have to equate f(x) to 0

to find the horizontal asymptote you need to find the limit of the function.
Which I honestly do not know how to do.

 

[Deleted member 4993]

Sorry, I wasn't aware. I'm new here and just needed quick help.

I know domain, x and y intercepts, and asymptotes when it comes to regular functions that don't involve sine, cosine, etc

Domain can be defined as the values that x can be and for range you answer the question what can y or in this case f(x) be. Correct

So what are the domain and range for y = 2cos(x) + x ?

x and y intercepts is when you set x and y = 0 respectively.
This is where I'm stuck.
I'm thrown off because it's a trig function
when x = 0 f(x) = 2
but when y or f(x) = 0 I don't know how to find x? Do I factor or what?

y = 2cos(x) + x

You cannot solve this in closed form. You can estimate the values through numerical analysis.

For the asymptotes
to find the vertical asymptotes you have to equate f(x) to 0

to find the horizontal asymptote you need to find the limit of the function.
Which I honestly do not know how to do.

For assymptotes, use a graphing calculator, (or go to wolframalfa.com) and plot the function. Then think about,

How is this plot different from y = cos(x)?

What are the assymptotes of y = cos(x)?

 

[JeffM]

Sorry, I wasn't aware. I'm new here and just needed quick help.

I know domain, x and y intercepts, and asymptotes when it comes to regular functions that don't involve sine, cosine, etc

Domain can be defined as the values that x can be and for range you answer the question what can y or in this case f(x) be.

What is confusing about this problem is that they ask you for the domain, but have already given it to you:

\(\displaystyle x \in \mathbb R\ and\ 0 \le x \le 2\pi.\)

Finding the range is easy. What are the maximum and minimum values of the cosine function over the given interval?
So what are the maximum and minimum values of 2cos(x) + x over the given integral?

x and y intercepts is when you set x and y = 0 respectively. Yes
This is where I'm stuck.
I'm thrown off because it's a trig function
when x = 0 f(x) = 2 Yes
but when y or f(x) = 0 I don't know how to find x? Do I factor or what? Again, this is confusing because there is no closed form solution. Have you been taught how to do approximations? Are you allowed to use a graphing calculator?

For the asymptotes Does the question ask whether there are asymptotes and, if so, what they are? Not every function has them.

to find the vertical asymptotes you have to equate f(x) to 0 This is quite wrong. You need to review the definition.

to find the horizontal asymptote you need to find the limit of the function. This is not quite right. You need to review the definition.
Which I honestly do not know how to do.

.