What is the limit as x approaches infinity of (3x-cos(x))/(2x+sin(x)) ?

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limit as x approaches infinity of (3x-cos(x))/(2x+sin(x))

x \to \infty lim (\frac{3 x - cos ( x )}{2 x + sin ( x )})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to \infty lim (\frac{3 x - cos ( x )}{2 x + sin ( x )})

Divide by highest denominator power:

\frac{3 - \frac{c o s ( x )}{x}}{2 + \frac{s i n ( x )}{x}}

= x \to \infty lim (\frac{3 - \frac{c o s ( x )}{x}}{2 + \frac{s i n ( x )}{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{c o s ( x )}{x} )}{lim _{x \to \infty} ( 2 + \frac{s i n ( x )}{x} )}

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

x \to \infty lim (2 + \frac{sin ( x )}{x}) = 2

= \frac{3}{2}

x \to \infty lim (\frac{4 x ^{2} + 5 x - 1}{x ^{2} - 7 x + 29})

x \to 1 lim (\frac{6 x + 1}{x - 1})

x \to 0 lim (\frac{tan ( x )}{x} cos (x))

x \to \infty lim ((\frac{1 + 9}{x})^{(\frac{x}{8})})

x \to \infty lim (- \infty + ln (2))

What is the limit as x approaches infinity of (3x-cos(x))/(2x+sin(x)) ?
The limit as x approaches infinity of (3x-cos(x))/(2x+sin(x)) is 3/2