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Math Help - a couple more calculus questions...

  1. #1
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    Question 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...
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  2. #2
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    Quote Originally Posted by bemidjibasser View Post
    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 \lim_{x \to 0} \frac{1}{x} - \frac{1}{x^2} \to - \infty. FOr the second

    f'(x) = <br />
\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  f'(3) doesn't exist.
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