What is the limit as x approaches infinity of (3x^2+10x-7)/(2x^2-5x) ?

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limit as x approaches infinity of (3x^2+10x-7)/(2x^2-5x)

x \to \infty lim (\frac{3 x ^{2} + 10 x - 7}{2 x ^{2} - 5 x})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to \infty lim (\frac{3 x ^{2} + 10 x - 7}{2 x ^{2} - 5 x})

Divide by highest denominator power:

\frac{3 + \frac{10}{x} - \frac{7}{x ^{2}}}{2 - \frac{5}{x}}

= x \to \infty lim (\frac{3 + \frac{10}{x} - \frac{7}{x ^{2}}}{2 - \frac{5}{x}})

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

x \to \infty lim (3 + \frac{10}{x} - \frac{7}{x ^{2}}) = 3

x \to \infty lim (2 - \frac{5}{x}) = 2

= \frac{3}{2}

y^{^{''}} - 6 y^{^{'}} + 25 y = - 45 cos (2 t) + 30 sin (2 t)

\frac{d}{d x} (ln (coth (x)))

\int \frac{cos ( 5 x )}{e ^{s i n (5 x)}} d x

\frac{d y}{d x} = 9 x + y

x \to 0 lim ((x - 1)^{2})

What is the limit as x approaches infinity of (3x^2+10x-7)/(2x^2-5x) ?
The limit as x approaches infinity of (3x^2+10x-7)/(2x^2-5x) is 3/2