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For x ? R, lim n→∞ ((x-3)/(x+2)) x = (A) e (B) e -1 (C) e -5 (D) e 5

For x ? R, limn→∞((x-3)/(x+2))x =
(A) e                                           (B) e-1
(C) e-5                                         (D) e5

Grade:12

1 Answers

askiitian.expert- chandra sekhar
10 Points
12 years ago

Hi Pallavi,

y=limx→∞((x-3)/(x+2))

=limx→∞((1-3/x)/(1+2/x))x

1 form

log y = log limx→∞((x-3)/(x+2))x

y = elimx→∞xlog((1-3/x)/(1+2/x))

y = elimx→∞[log((1-3/x)/(1+2/x))]/(1/x)

y = elimx→∞[log((1-3/x)- log(1+2/x))]/(1/x)

y =elimx→∞{[-3log((1-3/x)]/(-3/x)- [2log(1+2/x))](2/x)}

y = e-3-2 = e-5

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