What is the limit as x approaches 0 of (x^3+5x)/x ?

The limit as x approaches 0 of (x^3+5x)/x is 5

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limit as x approaches 0 of (x^3+5x)/x

x \to 0 lim (\frac{x ^{3} + 5 x}{x})

5

Solution steps

x \to 0 lim (\frac{x ^{3} + 5 x}{x})

Simplify

\frac{x ^{3} + 5 x}{x} : x^{2} + 5

= x \to 0 lim (x^{2} + 5)

Plug in the value

x = 0

= 0^{2} + 5

Simplify

= 5

\int_{0}^{x} \frac{1}{t ^{2} - 25} d t

y^{^{'}} = y + 3 t e^{t}, y (0) = 4

x \to 3 lim (x - 8)

\int (s^{3} + 3)^{2} (1 - s^{2})^{3} d s

y^{^{''}} - 16 y = 2 e^{4 x}

What is the limit as x approaches 0 of (x^3+5x)/x ?
The limit as x approaches 0 of (x^3+5x)/x is 5