Please help with derivatives- tearing my hair out!

[y2jerichoy2j]

\(\displaystyle \mbox{1. Use a calculator to approximate the following limit:}\)

. . . . .\(\displaystyle \displaystyle{\lim_{x\, \to\, 0}\, \dfrac{e^{11x}\, -\, 1}{x}}\)

\(\displaystyle \mbox{2. Let }\, G\, =\, 2f\, -\, g\, \mbox{ where the graphs of }\, f\, \mbox{ and }\, g\, \mbox{are shown}\)

. . . . .\(\displaystyle \mbox{in the graphic. Find }\, G'(3).\)

. . . . .

Can you guys please help me with these derivative questions? I really am confused and am having trouble in class. I thought the first one was 3+2, and the other was 60,000. Why am I wrong

 

[Deleted member 4993]

\(\displaystyle \mbox{1. Use a calculator to approximate the following limit:}\)

. . . . .\(\displaystyle \displaystyle{\lim_{x\, \to\, 0}\, \dfrac{e^{11x}\, -\, 1}{x}}\)

\(\displaystyle \mbox{2. Let }\, G\, =\, 2f\, -\, g\, \mbox{ where the graphs of }\, f\, \mbox{ and }\, g\, \mbox{are shown}\)

. . . . .\(\displaystyle \mbox{in the graphic. Find }\, G'(3).\)

. . . . .View attachment 3265

Can you guys please help me with these derivative questions? I really am confused and am having trouble in class. I thought the first one was 3+2, and the other was 60,000. Why am I wrong

Do you know how to use L'Hospital's rule?

 

[y2jerichoy2j]

Do you know how to use L'Hospital's rule?

what's that?

 

[Bob Brown MSEE]

Try Average of
(e^(11(0.01))-1)/(0.01)
and
(e^(11(-0.01))-1)/(-0.01)

 

[HallsofIvy]

It looks like Bob Brown MSEE, unlike either y2jericho2j or Subhotosh Khan, actually read the problem! The problem does NOT say "find the limit", it says "use a calculator to approximate the limit".

So, as Bob Brown MSEE suggests, evaluate it for some x close to 0.

 

[Deleted member 4993]

It looks like Bob Brown MSEE, unlike either y2jericho2j or Subhotosh Khan, actually read the problem! The problem does NOT say "find the limit", it says "use a calculator to approximate the limit".

So, as Bob Brown MSEE suggests, evaluate it for some x close to 0.

Going to the corner .... Denis move over....

 

[srmichael]

As for your second problem, G(x) = 2f(x) - g(x) and you are looking for G'(3).

First, what does G'(x) equal? Hint: Use the sum and difference rule of derivatives. And when you substitute 3 in for x into G'(x), how do we use the graph given to evaluate G'(3)? Hint: Plugging in a value for x into the derivative gets you what?

 

[stapel]

I thought the first one was 3+2, and the other was 60,000. Why am I wrong

Why did you think these were the answers? What was your reasoning?

We cannot help you see why you were wrong until we can see what you were doing. So please be complete. Thank you!