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Evaluate lim(xtooo) (1+(1)/(a+bx))^(c+dx...

Evaluate `lim_(xtooo) (1+(1)/(a+bx))^(c+dx)` , where a, b, c, and d are positive.

A

4

B

2

C

-1

D

0

Text Solution

Verified by Experts

The correct Answer is:
`e^(d//b)`
`underset(xtooo)lim(1+(1)/(a+bx))^(c+dx)=underset(xtooo)lim{(1+(1)/(a+bx))^(a+bx)}^((c+dx)/(a+bx))=e^(d//b)`
`{becauseunderset(xtooo)lim(1+(1)/(a+bx))^(a+bx)=e" and "underset(xtooo)lim(c+dx)/(a+bx)=d/b}`
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