What is the limit as x approaches infinity of (4x+1)/(12x^2-7) ?

The limit as x approaches infinity of (4x+1)/(12x^2-7) is 0

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limit as x approaches infinity of (4x+1)/(12x^2-7)

x \to \infty lim (\frac{4 x + 1}{12 x ^{2} - 7})

0

Solution steps

x \to \infty lim (\frac{4 x + 1}{12 x ^{2} - 7})

Divide by highest denominator power:

\frac{\frac{4}{x} + \frac{1}{x ^{2}}}{12 - \frac{7}{x ^{2}}}

= x \to \infty lim (\frac{\frac{4}{x} + \frac{1}{x ^{2}}}{12 - \frac{7}{x ^{2}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( \frac{4}{x} + \frac{1}{x ^{2}} )}{lim _{x \to \infty} ( 12 - \frac{7}{x ^{2}} )}

x \to \infty lim (\frac{4}{x} + \frac{1}{x ^{2}}) = 0

x \to \infty lim (12 - \frac{7}{x ^{2}}) = 12

= \frac{0}{12}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

\int \frac{1}{y + 3} d y

sin (x), 0.5

(3 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0, y (1) = 6

\frac{d y}{d t} = csc (y)

x \to 3 lim (x + 1 x + 2)

What is the limit as x approaches infinity of (4x+1)/(12x^2-7) ?
The limit as x approaches infinity of (4x+1)/(12x^2-7) is 0