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Math Help - Am I doing this right?

  1. #1
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    Am I doing this right?

    Let f(x)= xe^(x). Use the limit definition to compute f'(0) and find the equation of the tangent line at x=0

    f(x)= xe^(x)

    limit definition f'(x)= f(x+h)-f(x) / h as lim h-->0

    so

    f'(x) = (x+h)* (e^(x+h) - xe^(x) / h

    f'(0) = (0+h)* (e^(0+h) - xe^(0) / h

    = h*e(h)- 0 / h

    = e^(h) = e(0) =1

    So, the derivative is 1.

    Is this right?
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  2. #2
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    Quote Originally Posted by skboss View Post
    Let f(x)= xe^(x). Use the limit definition to compute f'(0) and find the equation of the tangent line at x=0

    f(x)= xe^(x)

    limit definition f'(x)= f(x+h)-f(x) / h as lim h-->0

    so

    f'(x) = (x+h)* (e^(x+h) - xe^(x) / h

    f'(0) = (0+h)* (e^(0+h) - xe^(0) / h

    = h*e(h)- 0 / h

    = e^(h) = e(0) =1

    So, the derivative is 1.

    Is this right?
    close enough from what I can discern from your syntax ... this might be a bit easier.

    f'(0) = \lim_{x \to 0} \frac{f(x) - f(0)}{x - 0}

    f'(0) = \lim_{x \to 0} \frac{xe^x - 0}{x - 0}

    f'(0) = \lim_{x \to 0} \frac{xe^x}{x}

    f'(0) = \lim_{x \to 0} e^x = e^0 = 1
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  3. #3
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    Thanks. BTW, Can I use that a limit definition to find derivative? I wasn't sure about it.
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