limit as x approaches infinity of (3x+9)/(2-x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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lim_{x→ ∞}(3x+92−x )

Solution

−3

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Solution steps

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lim_{x→ ∞}(3x+92−x )

Divide by highest denominator power: 3+9x 2x −1

=lim_{x→ ∞}(3+9x 2x −1 )

lim_x→a[f(x)g(x) ]=lim_x→af(x)lim_x→ag(x) , lim_x→ag(x)≠0
With the exception of indeterminate form

=lim_{x→ ∞}(3+9x )lim_{x→ ∞}(2x −1)

lim_{x→ ∞}(3+9x )=3

lim_{x→ ∞}(2x −1)=−1

=3−1

Simplify

=−3

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