Solve ;limit as x approaches zero (4-2x^2)1/2

Answer 1

We can solve this limit using the property of limits that says the limit of a product is the product of the limits.

First, let's take the limit of the expression inside the square root:

lim (4 - 2x^2) = 4

Next, let's take the limit of the entire expression:

lim [(4 - 2x^2)1/2]

= lim [(4 - 2x^2)1/2 * 1] (since 1 is a constant)

= lim [(4 - 2x^2)1/2] * lim [1] (using the property of limits mentioned above)

= 2 * 1

= 2

Therefore, the limit as x approaches zero of (4 - 2x^2)1/2 is equal to 2.