Lim of (1+ax)^1/x when x→∞: e^a

[abhishek.93]

Homework Statement

what is limit of (1+ax)^1/x w hen x → ∞ ??

Homework Equations

answer is e^a

The Attempt at a Solution

taking log i get
log y=1/x log(1+ax)

using l hospital i get

logy=-1/x2 X a/1+ax
so
putting x->∞


we get
logy=0
y=1

 

[HallsofIvy]

Homework Statement

what is limit of (1+ax)^1/x w hen x → ∞ ??

Oh! You mean (1+ ax)^(1/x)!

Homework Equations

answer is e^a

The Attempt at a Solution

taking log i get
log y=1/x log(1+ax)

using l hospital i get

logy=-1/x2 X a/1+ax
so
putting x->∞


we get
logy=0
y=1

You answer is correct.
$$e^a= \lim_{x\rightarrow 0} (1+ ax)^{1/x}$$

That is, the limit as x goes to 0 not infinity.