Find the limit.
\[
\lim _{u \rightarrow 5^{+}} \frac{4 u^{2}}{u-5}
\]

Answer

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Answer

Final Answer: \( \boxed{\infty} \)

Steps

Step 1 ：Find the limit as \( u \) approaches 5 from the positive side.

Step 2 ：Consider the behavior of the function as \( u \) gets closer to 5.

Step 3 ：The denominator approaches 0 as \( u \) approaches 5.

Step 4 ：The function will approach positive infinity if the numerator is positive, and negative infinity if the numerator is negative.

Step 5 ：The numerator is positive since it is a square of \( u \) multiplied by 4.

Step 6 ：Therefore, the limit should be positive infinity.

Step 7 ：\( \lim _{u \rightarrow 5^{+}} \frac{4 u^{2}}{u-5} = \infty \)

Step 8 ：Final Answer: \( \boxed{\infty} \)