Evaluate the limit: lim (x->0) (5x) / (x2 + 2x)

May 11, 2026Mathematics

ScanSolve AI Answer

May 11, 2026

Answer

$\frac{5}{2}$

Hey Victor, good to see you again.

Step 1: Substitute $x=0$ into the expression to check for an indeterminate form. $\frac{5(0)}{0^2 + 2(0)} = \frac{0}{0}$ Since this is an indeterminate form, we need to simplify the expression.

Step 2: Factor out $x$ from the denominator. $\lim_{x \to 0} \frac{5x}{x(x+2)}$

Step 3: Cancel out the common factor $x$ from the numerator and denominator. This is valid because $x \to 0$ means $x$ is approaching $0$ but is not equal to $0$ . $\lim_{x \to 0} \frac{5}{x+2}$

Step 4: Substitute $x=0$ into the simplified expression. $\frac{5}{0+2} = \frac{5}{2}$

The final answer is $\boxed{\frac{5}{2}}$ .

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Quick Answer

Hey Victor, good to see you again.
(5(0))/(0^2 + 2(0)) = (0)/(0) Since this is an indeterminate form, we need to simplify the expression.
_x 0 (5x)/(x(x+2)) Step 3: Cancel out the common factor x from the numerator and denominator.
This is valid because x 0 means x is approaching 0 but is not equal to 0.

Asked on May 11, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 11, 2026

Hey Victor, good to see you again. Step 1: Substitute x=0 into the expression to check for an indeterminate form. (5(0))/(0^2 + 2(0)) = (0)/(0) Since this is an indeterminate form, we need to simplify the expression. Step 2: Factor out x from the denominator. _x 0 (5x)/(x(x+2)) Step 3: Cancel out the common factor x from the numerator and denominator. This is valid because x 0 means x is approaching 0 but is not equal to 0. _x 0 (5)/(x+2) Step 4: Substitute x=0 into the simplified expression. (5)/(0+2) = (5)/(2) The final answer is (5)/(2). Send me the next one 📸

Asked on May 11, 2026Mathematics

ScanSolve AI AnswerAnswered on May 11, 2026

Hey Victor, good to see you again. Step 1: Substitute x=0 into the expression to check for an indeterminate form. (5(0))/(0^2 + 2(0)) = (0)/(0) Since this is an indeterminate form, we need to simplify the expression. Step 2: Factor out x from the denominator. _x 0 (5x)/(x(x+2)) Step 3: Cancel out the common factor x from the numerator and denominator. This is valid because x 0 means x is approaching 0 but is not equal to 0. _x 0 (5)/(x+2) Step 4: Substitute x=0 into the simplified expression. (5)/(0+2) = (5)/(2) The final answer is (5)/(2). Send me the next one 📸