Find the limit.
$lim_{u \to 5^{+}} \frac{4 u^{2}}{u - 5}$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\infty$

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 ： $lim_{u \to 5^{+}} \frac{4 u^{2}}{u - 5} = \infty$

Step 8 ：Final Answer: $\infty$