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