Problem

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

Solution

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: \( \boxed{\infty} \)

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Source: https://solvelyapp.com/problems/6VPMh92vzZ/

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