Find each limit, if it exists. If a limit does not exist, state that fact. If f ( x ) = x 2 + 3 , find f ' ( x ) by determining lim h → 0 f ( x + h ) − f ( x ) h .
Find each limit, if it exists. If a limit does not exist, state that fact. If f ( x ) = x 2 + 3 , find f ' ( x ) by determining lim h → 0 f ( x + h ) − f ( x ) h .
Solution Summary: The author explains that the difference quotient is equal to the slope of the secant line passing through (x+h)
Use the limit definition to find the derivative of the function.
f(x) = 4x + 5
First, find
f(a+h)-f(x)
h
Next, simplify the numerator.
Divide out the h.
So now, find the limit
lim
f(x+h)-f(x)
h
II
If 2x - 2s f(x) sx2 - 2x + 2 for x 2 0, find lim f(x).
x-2
Find each function value and the limit for
f(x)=15−6x^2/5+x^2.
Use −∞ or ∞ where appropriate.
Find:
(A) f(−10)
(B) f(−20)
(C) limx→−∞f(x
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