SOLUTION: I have two limit questions:
Find the derivative of f(x) = 2/x at x = -2.
Find the derivative of f(x) = -9/x at x = -8.
Please help!
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Question 984535: I have two limit questions:
Find the derivative of f(x) = 2/x at x = -2.
Find the derivative of f(x) = -9/x at x = -8.
Please help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first problem to get you started.
 = \frac{2}{x})
 = \frac{2}{x+h})
-------------------------------------------------------
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2}{x+h}-\frac{2}{x}}{h}\right))
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x}{x(x+h)}-\frac{2}{x}}{h}\right))
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x}{x(x+h)}-\frac{2(x+h)}{x(x+h)}}{h}\right))
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x-2(x+h)}{x(x+h)}}{h}\right))
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x-2x-2h}{x(x+h)}}{h}\right))
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{-2h}{x(x+h)}}{h}\right))
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{-2h}{xh(x+h)}\right))
-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{-2}{x(x+h)}\right))
-f(x)}{h}\right) = \frac{-2}{x(x+0)})
-f(x)}{h}\right) = \frac{-2}{x^2})
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Therefore, the derivative of f(x) is
Now plug in x = -2 to get
The final answer is
I'll let you do the other problem.
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