Evaluate the Limit

Problem

(lim_x→9)((40+√(,x))/√(,40+x))

Solution

1. Identify the limit expression and the value that x is approaching, which is x=9

2. Check for continuity by observing that the function ƒ(x)=(40+√(,x))/√(,40+x) is defined and continuous at x=9 because the denominator √(,40+9)=√(,49)=7 is non-zero.

3. Substitute the value x=9 directly into the expression to evaluate the limit.

L=(40+√(,9))/√(,40+9)

4. Simplify the square roots in the numerator and the denominator.

L=(40+3)/√(,49)

5. Calculate the final numerical value by performing the addition and the remaining square root.

L=43/7

Final Answer

(lim_x→9)((40+√(,x))/√(,40+x))=43/7

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