Question

Evaluate The Limit, If It Exists. (If It Does Not Exist, Enter NONE). Limₕ Right (1ₕ² -1/H Evaluate The Limit, If It Exists.

Answer 1

To evaluate the limit lim_(h\to0) ((1+h)^2 - 1)/h, we expand the numerator, simplify the expression, and find that the limit as h approaches zero is 2.

Step-by-step explanation:

The student's question involves evaluating the limit: lim_(h\to0) ((1+h)^2 - 1)/h. To solve this limit, we must apply algebraic simplification techniques to find the limit value as h approaches zero.

First, expand the squared term in the numerator:

(1+h)^2 = 1 + 2h + h^2.

Substitute back into the limit expression:

lim_(h\to0) (1 + 2h + h^2 - 1)/h.

Now, simplify by canceling the terms +1 and -1:

lim_(h\to0) (2h + h^2)/h.

Divide every term in the numerator by h:

lim_(h\to0) 2 + h.

Lastly, as h approaches zero, h term will become zero, so the limit is:

2.