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Michael M. answered • 02/26/22
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This problem says as h approaches zero, what does (5h - 1)/h approach.
So look at what happens when h approaches 0.
Plug in h = 0.1 into (5h - 1)/ h
Then plug in 0.01, 0.001, 0.0001, and 0.00001.
Find what (5h - 1)/ h is approaching approximately
Michael M.
Have you been taught the limit definition of a derivative: lim h->0 [f(x+h) - f(x) ] / h
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02/27/22
Mariam A.
Yes, I know this formula.
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02/27/22
Michael M.
Great, now this problem is a bit different. f(x) in this case is going to be 5^x. If we use the limit definition, we see that f ‘(x) = lim h-> 0 [5^(x+h) - 5^x] /h. This is pretty close to the problem. If you plug 0 for x, we get f ‘(0) = lim h-> 0 [5^(0+h) - 5^0] /h which simplifies to f ‘(0) = lim h-> 0 [5^(h) -1] /h. Therefore, we see that the answer is just f ‘(0) where f(x) = 5^x. This will give you an answer of ln(5) which should be about what you got.
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02/27/22
Mariam A.
How f(x) = 5^x? and to get ln(5) did we use derivative here?
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02/27/22
Mariam A.
Is there a quickest way to solve this problem if I'm in an exam?02/27/22