# How do you find #lim (x+1)^(3/2)-x^(3/2)# as #x->1^+#?

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To find the limit of (x+1)^(3/2) - x^(3/2) as x approaches 1 from the right, we can use the concept of limits.

First, let's simplify the expression by using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Applying this formula, we have: (x+1)^(3/2) - x^(3/2) = [(x+1) - x][(x+1)^(1/2) + x^(1/2) + x^(1/2)]

Simplifying further, we get: (x+1)^(3/2) - x^(3/2) = (1)(2x^(1/2) + 1)

Now, we can take the limit as x approaches 1 from the right: lim (x+1)^(3/2) - x^(3/2) as x->1^+ = lim (2x^(1/2) + 1) as x->1^+ = 2(1^(1/2)) + 1 = 2 + 1 = 3

Therefore, the limit of (x+1)^(3/2) - x^(3/2) as x approaches 1 from the right is 3.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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