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Find the limit.

lim x→∞ 2−e^x/2+9e^x

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I am sure you meant:
lim (2- e^x)/(2+9e^x)
divide each by e^x

= Lim (2/e^x - 1)/(2/e^x + 9)
now as x→∞ , e^x ---> 0
and we approach the value

(0-1)/(0+9) = -1/9

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