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given the fact that f'(69)=3 , calculate lim h->0

Note that (f(69+h)-f(69))/h is the definition of f'(69), and that is known to be 3.

The only difference h is being multiplied by 9 on the top and 2 on the bottom.

On the top, the measurements are being taken 9 times farther way,
so the answer comes out 9 times as large.

On the bottom, h is multiplied by 2, so the answer turns out to be 1/2 of what it should be.

That makes the answer be f'(69)9/2 = 3*9/2 = 27/2 = 13.5.


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