!<Answer>!
To solve the limit of the given expression, we can simplify it step by step.
Step 1: Simplify the expression inside the square root:
√x + 1/√x = (√x * √x + 1)/√x = (x + 1)/√x
Step 2: Rewrite the expression:
(x + 1)/x * (x + 1)/√x
Step 3: Multiply the fractions:
(x + 1)(x + 1)/(x * √x)
Step 4: Simplify the expression:
(x^2 + 2x + 1)/(x * √x)
Step 5: Rewrite the expression as a single fraction:
(x^2 + 2x + 1)/x√x
Step 6: Simplify the expression further:
(x + 1)^2/x√x
Step 7: Take the limit as x approaches 0:
As x approaches 0, the expression (x + 1)^2 becomes (0 + 1)^2 = 1^2 = 1. The expression x√x becomes 0 * 0 = 0.
Therefore, the limit of the given expression as x approaches 0 is 1/0, which is undefined.
In summary, the limit of the expression (x + 1/x) * (√x + 1/√x) as x approaches 0 is undefined.
~ Sun
