lim h->0 (((1/(1+h))-1)/h
I don't understand how the answer is -1 shouldn't it be 0?
Just look at the part
1/(1+h) - 1
= 1/(1+h) - 1/1
using a common denominator of 1+h
we get
(1 - 1+h)/(1+h)
= -h/(1+h)
so lim h->0 (((1/(1+h))-1)/h
= lim(-h/(1+h))/h
doesn't the h cancel?
so now we have
Lim -1(1+h) as h -->0
= -1/(1+0)
= -1
Got it, thanks :)
To find the limit of the expression as h approaches 0, let's simplify the expression step by step:
First, let's simplify the numerator:
(1/(1+h)) -1
To simplify this, we need to find a common denominator. The common denominator is (1+h):
(1/(1+h)) - (1*(1)/(1+h))
Now, combine fractions with the same denominator:
[(1 - (1+h))/(1+h)]
Simplifying the numerator:
(1 - 1 - h)/(1+h) = (-h)/(1+h)
Next, let's simplify the whole expression:
((-h)/(1+h))/h = (-h)/(h * (1+h))
We can cancel out the h in the numerator and denominator:
-1/(1+h)
Now that we have simplified the expression, let's find the limit as h approaches 0:
lim h->0 -1/(1+h)
Plugging h = 0 into the expression:
-1/(1+0) = -1
Therefore, the limit of the expression as h approaches 0 is -1, not 0.