What is the limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x) ?

The limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x) is 3

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limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x)

x \to 0 lim (\frac{7 x ^{5} + 5 x ^{2} + 12 x}{3 x ^{5} + 4 x})

3

Solution steps

x \to 0 lim (\frac{7 x ^{5} + 5 x ^{2} + 12 x}{3 x ^{5} + 4 x})

Simplify

\frac{7 x ^{5} + 5 x ^{2} + 12 x}{3 x ^{5} + 4 x} : \frac{7 x ^{4} + 5 x + 12}{3 x ^{4} + 4}

= x \to 0 lim (\frac{7 x ^{4} + 5 x + 12}{3 x ^{4} + 4})

Plug in the value

x = 0

= \frac{7 \cdot 0 ^{4} + 5 \cdot 0 + 12}{3 \cdot 0 ^{4} + 4}

Simplify

\frac{7 \cdot 0 ^{4} + 5 \cdot 0 + 12}{3 \cdot 0 ^{4} + 4} : 3

= 3

x^{2} - 3 x y = 10

y^{^{'}} = \frac{sec ( y )}{( x - 3 ) ^{2}}

n = 0 \sum \infty \frac{2}{1}

\frac{\partial}{\partial x} (4 x + y)

\frac{d}{d x} ((\frac{2}{x} - \frac{1}{x ^{2}})^{\frac{1}{2}})

What is the limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x) ?
The limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x) is 3