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Find the limits: (a) underset(x to oo)...

Find the limits:
(a) `underset(x to oo)lim (1+1//x)^(7x)`, (b) `underset(x to 0)lim (1+x)^(1//3x)`
(c ) `underset(x to oo)lim ((x)/(1+x))^(x)`, (d) `underset(x to oo)lim (1+k//x)^(mx)`
(e ) `underset(x to 0)lim (ln (1+x))/(3^x-1)` (f) `underset(x to 0)lim (e^(4x)-1)/(tan x)`
(g) `underset(x to 0)lim (ln (a+x)-ln a)/(x)` (h) `underset(x to 0)lim (e^(x)-e^(-x))/(sin x)`
(i) `underset(x to e)lim (ln x-1)/(x-e)`

Text Solution

Verified by Experts

The correct Answer is:
`(b) e^(1/3); (c) e^(-1); (d) e^(mk) ; (f) 4; (g) 1/a ; (h) 2`
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