✏️ Adventure 11 — Taylor Series
Mimics the SS11 PDF layout (captions above boxes + Taylor polynomial lines), in SS4 style.
Taylor Series for f(x)
Around x=0
f(0)
x
f'(0)
x
f''(0)
x^2/2!
f'''(0)
x^3/3!
f''''(0)
x^4/4!
f'''''(0)
x^5/5!
f''''''(0)
x^6/6!
1 + x/1 + x^2/2! + x^3/3! + x^4/4! + x^5/5! + x^6/6! + …
;
Fill in the Values ==>
Taylor Series for ex
e1 = 2.718
;
value for x=1;
;
Compute Cumulative value ==>
e0
e0
e0
e0
e0
e0
e0
1 + x/1 + x2/2! + x3/3! + x4/4! + x5/5! + x6/6! + …
;
Fill in the Values ==>
Taylor Series for cos(x)
cos(pi/3)=0.50;
value for pi/3;
;
Compute Cumulative value ==>
cos(0)
-sin(0)
-cos(0)
sin(0)
cos(0)
-sin(0)
-cos(0)
1
0
-x2/2!
0
x4/4!
0
-x6/6!
;
Fill in the Values ==>
Taylor Series for sin(x)
x = pi/3
sin(pi/3) = 0.866
value for pi/3;
;
Compute Cumulative value ==>
sin(0)
cos(0)
-sin(0)
-cos(0)
sin(0)
cos(0)
-sin(0)
0
x
0
-x3/3!
0
x5/5!
0
1
i
i2
i3
i4
i5
i6
Taylor Series for ex
Taylor Series for eix
cos x
+ i sin x
eix = cos x + i sin x
(values)
(values)
eix =
Fill Values
Sample Solution (PNG)
