Posted by K on Thursday, February 2, 2012 at 5:59pm.
Find the limit.
lim
h → 0 square root (49 + h) − 7 / h
Note: Only 49 +h are under square root.

calculus  Steve, Friday, February 3, 2012 at 10:50am
Use L'Hopital's Rule:
sqrt(49+h) = (49+h)^1/2
= 49^1/2 + 1/2 49^1/2 * h + (1/2)(1/2)/2 49^3/2 h^2 ...
= 7 + h/2*7 + ... (higher powers of h)
so,(sqrt(49+h)7)/h = 1/14 + ... (powers of h, all being 0)
so, limit as h>0 is 1/14
Note that if y=√x, y' = 1/2√x, so y'(7) = 1/14

calculus  PS  Steve, Friday, February 3, 2012 at 10:50am
Ummm. make that Binomial Theorem, not L'Hopital's Rule
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