Thread: a couple more calculus questions...

1. a couple more calculus questions...

I am a little unsure if I have these correct. Here goes:
1. let g(x)=1/x - 1/x^2. Find the limit as x approaches 0. I came up with 0, but I also am thinking it might be -infinity. Are either of theses right?

2. let h(x)= x^2 if x< 3 and 2x+3 if x>3. Find f'(3). I found f'(3) to be equal to 6. Am I on the right track here or not quite. I know I would need to differentiate the functions, but then I'm a little fuzzy...
Thanks for the help...

2. Originally Posted by bemidjibasser
I am a little unsure if I have these correct. Here goes:
1. let g(x)=1/x - 1/x^2. Find the limit as x approaches 0. I came up with 0, but I also am thinking it might be -infinity. Are either of theses right?

2. let h(x)= x^2 if x< 3 and 2x+3 if x>3. Find f'(3). I found f'(3) to be equal to 6. Am I on the right track here or not quite. I know I would need to differentiate the functions, but then I'm a little fuzzy...
Thanks for the help...
For the first g(0) is undefined. Look at the graph and you'll see $\displaystyle \lim_{x \to 0} \frac{1}{x} - \frac{1}{x^2} \to - \infty$. FOr the second

$\displaystyle f'(x) = \left\{\begin{array}{cl}2x,&\mbox{ if }x < 3\\2, & \mbox{ if } x>3\end{array}\right.$

Since the left and right limits are different, then $\displaystyle f'(3)$ doesn't exist.