Asked by Tyler
Evaluate the following limit, if it exists:
lim h-->0 ((sqrt9+h)-3/(h)
lim h-->0 ((sqrt9+h)-3/(h)
Answers
Answered by
Steve
if f(x) = √x
the limit is f'(9)
f'(x) = 1/(2√x)
f'(9) = 1/6
If you must evaluate the limit, just use the binomial theorem:
(9+h)^(1/2) = 9^(1/2) + (1/2)/1! 9^(-1/2)h + (1/2)(-1/2)/2! 9^(-3/2) h^2 + ...
subtract 3, divide by h, and set h=0
the limit is f'(9)
f'(x) = 1/(2√x)
f'(9) = 1/6
If you must evaluate the limit, just use the binomial theorem:
(9+h)^(1/2) = 9^(1/2) + (1/2)/1! 9^(-1/2)h + (1/2)(-1/2)/2! 9^(-3/2) h^2 + ...
subtract 3, divide by h, and set h=0
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