Square All
How do you evaluate the limit as h->0 of the square root of (3-h) minus the square root of 3 all over h?
I hope this shows up correctly on your screen
lim √(3-h) - √(3)
h->0 h
So. Limit as h approaches 0 of the difference, square root of (3-h) minus square root of 3, all over h.
I can evaluate this by using L'Hopital's rule, but can anyone give me a secondary way to evaluate this limit?
Recognize that it looks similar to the limit definition of the derivative
f'(x) = lim[ (f(x+h) - f(x)) / h; h goes to 0 ]
Clearly the given is the derivative of the square root evaluated at 3 as approached from the left.
So, f(x) = sqrt(x); f'(x) = 0.5 / sqrt(x)
and lim[ (sqrt(3-h) - sqrt(3)) / h; h goes to 0 ] = f'(3)
= 0.5 / sqrt(3)
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