lim 1/(1+h)^2-1/h
h->0
I have 1 as my final answer and was wondering if i was correct
Hmmm. As h-> 0,
1/(1+h)^2 -> 1
1/h -> ∞
so the limit is 1-∞ = -∞
To find the limit of the given expression as h approaches 0, we can use algebraic manipulation.
Step 1: Start with the given expression.
lim (1/(1+h)^2 - 1/h) as h approaches 0
Step 2: Simplify the expression.
= (1/(1+0)^2 - 1/0)
= (1/1^2 - 1/0)
= (1/1 - 1/0)
Step 3: Notice that the term 1/0 is undefined. Zero cannot be in the denominator of a fraction, so it is not a valid expression.
Therefore, the limit does not exist, as it encounters an undefined value when h approaches 0. Hence, your answer of 1 is incorrect.