The Manga Guide to Calculus

Since we now know

lnh x z

n

( )

≈ −

1

2

2

,

we get

h x e

n

z

( )

≈ −

−

1

2

2

.

That’s it!

If you are afraid that the higher-degr terms of

x

3

and more that aear in the Taylor expansion

of ln might aect the shape of h

n

(x) (n: large

enough),actuay calculate h

n

(x), using

ln 1

1

2

1

3

2 3

+

( )

≈ − +t t t t

You wi find that the term of z

4

has n in the

denominator of its coeicient and converges to

zero, or disaears, when n → ∞.

As for the normal

distributions, can we

aly them to things

other than coin

fliing?

What Does Taylor Expansion Te Us? 175

176 Chapter 5 Le