stupid question

ex is defined as

e^x= \frac{x^0}{0!}+\frac{x^1}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+..........

for x=0,

e^0= \frac{0^0}{0!}+\frac{0^1}{1!}+\frac{0^2}{2!}+\frac{0^3}{3!}+..........

but we know that e0 is 1

So

1= \frac{0^0}{0!}+\frac{0^1}{1!}+\frac{0^2}{2!}+\frac{0^3}{3!}+..........

1=0^0

What's the folly??

11 Answers

11
virang1 Jhaveri ·

the expansion is ex is alway written as
e^x= \frac{1^}{0!}+\frac{x^1}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+..........
And not
e^x= \frac{x^0}{0!}+\frac{x^1}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+..........

11
Anirudh Narayanan ·

No da x0 is always simplified and written as 1 for convinience

anyways, the source is reliable.....i doubt if u cud get a more reliable source than wiki

http://upload.wikimedia.org/math/0/b/c/0bc08045195dc823c22d1fa283cb0759.png

11
Mani Pal Singh ·

http://www.math.com/tables/expansion/exp.htm

have a look at this 1
the 1st 1 u r making mistake in
and u r confusing between the 1st and the 3 rd 1

hope this could help

11
Anirudh Narayanan ·

i didn't get u mani

see the expansion of ex is

e^x=\sum_{n=0}^{\infty}{\frac{x^n}{n!}}

so for x=0, why Doesn't that expansion hold good?

11
Mani Pal Singh ·

THIS IS THE EXPANSION OF ex
PUT 0 HERE

THIS MIGHT BE HELPFUL

11
Anirudh Narayanan ·

Why are dodging the original definition??

ex= x0/0! + x1/1! +x2/2! + x3/3! + ................

And haven't we learnt that (cos90°).(tan90°)≠1 even though sin90°=1??

11
Mani Pal Singh ·

even though we can cancel the two cos90°s??[5][5][5][5][5]

bHAI JO PEHLI DEFINITION DI HAI WOH ORIGINAL HAI

PEHLE TU YEH BATA
KI
TU PAANGE LE RAHA HAI
YA
FIR

YEH TERE POTENTIAL OUTSTANDING AND OUT OF THE WORLD BRAIN KI KHOJ HAI[7][7][7]

1
°ღ•๓яυΠ·

this defination is for x> 0

:P

11
Mani Pal Singh ·

11
Anirudh Narayanan ·

allright allright...........sorry for the poor English

edited it now and so i implore thee to answer my question

apun ki brain ka khoj baadh me karenge

11
Anirudh Narayanan ·

arey, what is this??

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