Question

Evaluate lim h-->0 f(x0+h) - f(x0)/ h for the given x0 and function f. f(x) = 5/x for x0 = 6. A) Does not exist; B) -30; C) -5/36; D) 5/6

Answer 1

So we're trying to calculate the derivative of f(x) = 5 / x at x0 = 6

The first step is to plug the function and x0 into the limit:

We get

\[\lim \frac{ \frac{ 5 }{ 6+h} + \frac{ 5 }{ 6 } }{ h }\]

The next step (and the hard step) is the simplify by combing the fracations

\[\lim \frac{ \frac{ (5)(6) - (5)(6+h) }{ (6)(6+h) } }{ h}\]

Simplify it

\[\lim \frac{ \frac{ 30-30-5h }{ (6)(6+h) } }{ h }\]

At this point, it shouldn't be too terrible to simplify it a bit more... let me know what you get.

Answer 2

i got -5/36 (C) thank you so much.