Calculus 1 problem: functions

[Pliskinus]

Im doing some older exams that my professor has provided, but I havent got the solutions for this one. Can someone help confirm that the solution Ive arrived at is correct?

 

[Deleted member 4993]

Im doing some older exams that my professor has provided, but I havent got the solutions for this one. Can someone help confirm that the solution Ive arrived at is correct?

View attachment 19314

Please tell us the "steps" you took to arrive at the location of the solution.

 

[LCKurtz]

What is [MATH]\lim_{x \to 0}\frac{e^x -1}{x}[/MATH]? Show us what happens when you try to work it out.

 

[HallsofIvy]

Yes, that is correct, However, just picking an answer, even if it is correct, is not enough. What the others here are trying to tell you is that you have to be able to justify your answer! How do you know that g(x) is continuous at x= 0?