Find the limit lim _(xarrow 0)(sqrt (x+5)-sqrt (5))/(x) (1)/(2sqrt (5)) infty (1)/(4) 1 DNE

## Step 1: Rationalizing the Numerator### To evaluate the limit, we'll rationalize the numerator by multiplying the expression by . This will help simplify the expression and eliminate the indeterminate form as approaches 0.## Step 2: Simplifying the Expression### After multiplying, the numerator becomes , and the denominator becomes . We can then cancel out the terms in the numerator and denominator, leaving .## Step 3: Evaluating the Limit### Now, we can substitute into the simplified expression: .