Taylor Series to know

Question 1

e^x (Exponential Series)

Answer 1

sum k=[0, inf): (x^k)/(k!)
on R

Question 2

sin(x) (Sine Series)

Answer 2

sum k=[0, inf): [(-1)^k * x^(2k+1)] / [2k+1]!
on R

Question 3

cos(x) (Cosine Series)

Answer 3

sum k=[0, inf): [(-1)^k * x^(2k)] / [2k]!
on R

Question 4

1/(1-x) (Reciprocal Series)

Answer 4

sum k=[0, inf): x^k
on |x|<1

Question 5

ln(x+1) (Logarithm Series)

Answer 5

sum k=[1, inf): (-1)^(k+1) * [x^k]/[k]
on -1 < x < 1

Question 6

arctan(x) (Arctangent Series)

Answer 6

sum k=[0, inf): (-1)^k * [x^(2k+1)] / [2k+1]
on |x| <= 1

Question 7

arcsin(x) (Arcsine series)

Answer 7

sum k=[0, inf): x^(2k+1) * [2k]! / [(4^k) * (k!)^2 * (2k+1)]
on |x| <= 1

Question 8

sinh(x) (Hyperbolic Sine Series)

Answer 8

sum k=[0, inf): [x^(2k+1)] / [(2k+1)!]
on R

Question 9

cosh(x) (Hyperbolic Cosine Series)

Answer 9

sum k=[0, inf): [x^(2k)] / [(2k)!]
on R

Question 10

f(x) (approximately)

Answer 10

sum k=[0, inf): (x-a)^k * [f^k(a)] / k!