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Math Help - Geometric interpretation of a limit?

  1. #1
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    Geometric interpretation of a limit?

    Hi everyone,
    I came across this problem in my homework and I'm not sure how to answer it.

    Draw a geometric interpretation of the limit lim h->0 (8(1/2+h)^8 - 8(1/2)^8)/h

    Can anyone help? Thank you
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  2. #2
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    Quote Originally Posted by EucalyptusMint View Post
    Hi everyone,
    I came across this problem in my homework and I'm not sure how to answer it.

    Draw a geometric interpretation of the limit lim h->0 (8(1/2+h)^8 - 8(1/2)^8)/h

    Can anyone help? Thank you
    Let f(x) be 8x^8. Then (1/2, 8(1/2)^8)= (1/2, f(1/2)) and (1/2+ h, 8(1/2+h)^8)= (1/2+ h, f(1/2+ h)) are two points on the graph of y= f(x). (8(1/2+h)^8- 8(1/2)^8)/h is the slope of the line through them. As h goes to 0, what happens to that line?
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  3. #3
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    The slope would decrease since the second point (1/2 +h, f(1/2+h) would approach the first point, right?

    I'm still a bit confused on what it means by "geometric interpretation"
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