# Thread: Geometric interpretation of a limit?

1. ## 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

2. Originally Posted by EucalyptusMint
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 $\displaystyle 8x^8$. Then $\displaystyle (1/2, 8(1/2)^8)= (1/2, f(1/2))$ and $\displaystyle (1/2+ h, 8(1/2+h)^8)= (1/2+ h, f(1/2+ h))$ are two points on the graph of y= f(x). $\displaystyle (8(1/2+h)^8- 8(1/2)^8)/h$ is the slope of the line through them. As h goes to 0, what happens to that line?

3. 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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