What is the limit as x approaches infinity of (3x^2-7x)/(5x^2+7) ?

The limit as x approaches infinity of (3x^2-7x)/(5x^2+7) is 3/5

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limit as x approaches infinity of (3x^2-7x)/(5x^2+7)

x \to \infty lim (\frac{3 x ^{2} - 7 x}{5 x ^{2} + 7})

\frac{3}{5}

Decimal Notation

0.6

Solution steps

x \to \infty lim (\frac{3 x ^{2} - 7 x}{5 x ^{2} + 7})

Divide by highest denominator power:

\frac{3 - \frac{7}{x}}{5 + \frac{7}{x ^{2}}}

= x \to \infty lim (\frac{3 - \frac{7}{x}}{5 + \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} ( 3 - \frac{7}{x} )}{lim _{x \to \infty} ( 5 + \frac{7}{x ^{2}} )}

x \to \infty lim (3 - \frac{7}{x}) = 3

x \to \infty lim (5 + \frac{7}{x ^{2}}) = 5

= \frac{3}{5}

x \to 5 - lim (\frac{sin ( ( x - 7 ) ( x - 5 ) )}{x - 5})

x \to 1 lim (1 + x^{\frac{1}{1 - x}})

h \to 0 lim (\frac{\frac{2}{8 + h} - 8}{h})

x \to - 2 lim (- x^{2} + 3 x + 4)

x \to 0 lim (a^{m x})

What is the limit as x approaches infinity of (3x^2-7x)/(5x^2+7) ?
The limit as x approaches infinity of (3x^2-7x)/(5x^2+7) is 3/5