Solve ;limit as x approaches zero (4-2x^2)1/2
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.
To solve the limit of (4-2x^2)^1/2 as x approaches zero, we can plug in the value of x and see what the expression approaches.
When we substitute x = 0 into the expression, we get:
(4 - 2(0)^2)^1/2
(4 - 2(0))^1/2
(4 - 0)^1/2
4^1/2
√4
2
So, the limit of (4-2x^2)^1/2 as x approaches zero is equal to 2.