PLEASE HELP the approximate value of y=sqrt(3+e^x) at x=0.08, obtained from the tangent to the graph at x=0, is
1) 2.01
2) 2.02
3) 2.03
4) 2.04
5) 2.05
explanation would be greatly appreciated

Question

mathmale · Answer

this is "linear approximation."  Have you used this method before?
You are asked to approximate the value of  y=sqrt(3+e^x) at x=0.08.  Let y = f(x).

Then the relevant linear approx. formula is 

$$f(x)approxf(x _{0})+f'(x _{0})*(x-x _{0})$$

mathmale · Answer

Here, f(x) =  Sqrt(3+e^x) and x_0 is 0.08.

anonymous · Answer

i have never used this method by i've heard of "linear approximations"

mathmale · Answer

What method is your teacher (or your online instruction) using for linear approximations?
Note that you are asked to approximate the value of the given function at x=0.08 using the tangent line.  The formula I have given you does exactly that.  
\[f'(x _{0})\

mathmale · Answer

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anonymous · Answer

I would approximate x=0.08 to x$$\approx$$0

anonymous · Answer

and solve with a point slope formula

mathmale · Answer

No, Caden.  You are asked to approximate the value of the given function when x=0.08.
If you want to use the point-slope form of the equation of a straight line, you'll still need to determine the slope of the line; how would you do that?

anonymous · Answer

i'm not sure that was just the first thought i had to answering this question

mathmale · Answer

What is the name of the TOPIC you are studying right now?  I call it "linear approximations."  But then I realize you probably haven't studied calculus yet.  What is the name of your math course?

anonymous · Answer

ap calculus ab

anonymous · Answer

I'm doing a practice problem and i got extremely confused so i came here

mathmale · Answer

advanced placement calculus.  Wow. congrats.  
But this means you are responsible for topics such as "linear approximations."
\
If you give me a function and a particular x value (such as 0.08)

anonymous · Answer

are linear approximations something i should have learned before calculus?

mathmale · Answer

No, Caden, but rather "linear approximations" are an application of calculus in your first course in the subject.  Perhaps your teacher is using a different name for this.