Posted by K on Thursday, February 2, 2012 at 5:59pm.
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
Ummm. make that Binomial Theorem, not L'Hopital's Rule
Related Questions
calc 3 - Use polar coordinates to find the limit. [If (r, θ) are polar ...
calculus - State which of the conditions are applicable to the graph of y = f(x...
Math - Math.. find limit help? Find the given limit. (x→ 1)lim: (...
Cal-Help Please - Evaluate the limit, if it exists. lim , 3 − square ...
calculus please help - lim y→−1 (sqrt(y^2+8)-3)/y+3 find ...
Math: Limits - Estimate the limit numerically. lim as x→(approaches to...
Math find the limit. - Evaluate the limit, if it exists. (If it does not exist, ...
Calculus - (a) By graphing the function f(x) = (cos 2x − cos x)/x2 and...
Calculus - (a) By graphing the function f(x) = (cos 2x − cos x)/x2 and...
math,help - how do i find the following: is there a formula for this? Problem #...
For Further Reading
