calculus (limits)
posted by John .
lim h>0 sqrt(1+h)1/h
not sure how to factor this; not allowed to use L'Hopital's Rule. (that isn't taught at my school until Calc II & I'm in Calc I).

calculus (limits) 
Damon
I bet you mean
lim h>0 [sqrt(1+h)1] /h
One way:
I guess you know how to take derivatives
d/dx (x)^.5 = .5 (x^.5)
(of course right there you can say
x^.5 at x = 1 so your result is
.5/1 = .5
so
d (x^.5) = .5 x^.5 dx
so
d (sqrt (x)) dx = .5 dx/sqrt(x)
d sqrt(1+h) dx = .5 dx/sqrt(1+h)
if h >0
d sqrt(1+h)dx = .5 sqrt(1)h/sqrt(1)
= .5 h
so sqrt(1+h) > 1 + .5 h
sqrt(1+h)1 > .5 h
divide by h and get
.5
series for sqrt(x) for x approximately 1 is
= 
calculus (limits) 
John
I do know how to take derivatives however the course I'm in hasn't taught them yet (long story) so I can't use derivatives in finding the solution; I have to factor.
So perhaps a better question is: how do I factor the above expression in a way that will allow me to find the limit? 
calculus (limits) 
Damon
Taylor series for f(x + a ) for x approximately 1 is
f(x)= f(1) + f'(1)(xa) + f''(xa)^2/2 ...
for f(x) = sqrt (x)
f(1) = (1)^.5 = 1
f'(1) = .5 (1)^.5 = .5
f"(x) = .25(1)^1.5 etc = .25
f(x+h) = 1 + .5*h .25 h^2 /2 etc
subtravt 1
.5h .125 h^2 tc
divide by h and let h>0
.5  .125 h > .5 
calculus (limits) 
Damon
factor (x+h)^.5 ?
I do not know how
Somehow you have to know that sqrt(1+h) > 1 + .5 h +..... 
John needs analysis help 
Damon
Perhaps someone else knows how

calculus (limits) 
Reiny
rationalize the numerator, that is, multiply top and bottom by (√(1+h) + 1)/(√(1+h) + 1)
lim (√(1+h)  1)/h as h >0
= lim (√(1+h)  1)/h (√(1+h) + 1)/(√(1+h) + 1)
= lim (1+h 1)/[h( (√(1+h) + 1)/h)]
= lim 1/( (√(1+h) + 1)
= 1/(1+1) = 1/2
Respond to this Question
Similar Questions

Calc Limits
lim (1+x)^1/x. Give an exact answer. x>0 This reads: The limits as x approaches zero is (1 plus x) to the 1 divided by x. The log of each term is (1/x) ln (1 + x) = ln (1+x)/x Using L'Hopital's rule for the limit of f(x)/g(x), … 
limit calc question
2 questions!!! 1. Limit X approaching A (X^1/3a^1/3)/ xa 2. LiMIT x approaching 0 (1/3+x – 1/3) /x On the first, would it help to write the denominator (xa) as the difference of two cubes ((x^1/3 cubed  a^1/3 cubed) second. use … 
Calc. Limits
Are these correct? lim x>0 (x)/(sqrt(x^2+4)  2) I get 4/0= +/ infinity so lim x>0+ = + infinity? 
calculus, limits, l'hopital
Using l'hopital's rule, find the limit as x approaches infinity of (e^(6/x)6x)^(X/2) I know l'hopital's rule, but this is seeming to be nightmare. I just don't seem to get anywhere. 
calculus, limits, l'hopital
Using l'hopital's rule, find the limit as x approaches zero of (e^(6/x)6x)^(X/2) I know l'hopital's rule, but this is seeming to be nightmare. I just don't seem to get anywhere. I mistyped the first time I posted this question. 
calc
Use L’Hopital’s rule to find the limit of this sequence (n^100)/(e^n) ...If you do L'Hop. Rule it would take forever, right? 
Calculus
Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. … 
Calculus
Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. … 
AP Calc (Limits)
I'm trying to factor this equation in order to find its limit, but I'm not sure how to go about it. I can get the answer by graphing on a calculator but I need to do it without one. Function: F(x)=(x^236)/(sqrt(x^212x+36)) left, … 
Limits calc 1
Lim X➡️2. X+2/x^3+8 How do I factor out the bottom?