**Question about Calculus (Limit)...?**

**In my Textbook, the question is:**

**Show that : lim (1+1/x)^x= e as x--> Infinity**

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`Put 1 + 1/x = t =gt 1/x = t - 1 =gt x = 1/(t-1)`

Calculate logarithms both sides:

`ln x = ln(1/(t-1))`

`` Use quotient property of logarithms:

ln x = ln1 - ln (t-1)

ln 1 = 0 =>

`ln x = - ln (t-1)`

Write the function using variable t:

t^(1/(t-1)) => `lim_(t-gtoo)` `t^(1/(t-1))` = `lim_(t->oo)` `(1 + t - 1)^(1/(t-1)) ` (you must add and subtract 1 in the brackets and create the form `(1+a_n)^(1/a_n)).` **Calculate the limit:**

** `lim_(t->oo)` [1 + (t-1)]^1/(t-1) = e**

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