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Question 1

DL e^x

Answer 1

1+x+x²/2+…+x^n/n! + o(x^n)

Question 2

DL 1/1+x

Answer 2

1-x+x²-x³+…+(-1)^n x^n+o(x^n)

Question 3

DL 1/1-x

Answer 3

1+x+x²+x³+…+x^n+o(x^n)

Question 4

DL ln(1+x)

Answer 4

x-x²/2+x³/3-….+(-1)^(n-1)x^n/n +o(x^n)

Question 5

DL ln(1-x)

Answer 5

-x-x²/2-x³/3-….-x^n/n +o(x^n)

Question 6

DL cosx

Answer 6

1-x²/2!+x^4/4!-…+(-1)^n x^2n/(2n)! +o(x^2n+1)

Question 7

DL sinx

Answer 7

x-x³/3!+x^5/5!-…+(-1)^n x^2n+1/(2n+1)! +o(x^2n+1)

Question 8

DL tanx

Answer 8

x+x³/3+2x^5/15+17x^7/315+o(x^8)

Question 9

DL arctanx

Answer 9

x-x³/3+x^5/5-…+(-1)^n x^2n+1/(2n+1) +o(x^2n+2)

Question 10

DL chx

Answer 10

1+x²/2!+x^4/4!+…+x^2n/(2n)! +o(x^2n+1)

Question 11

DL shx

Answer 11

x+x³/3!+x^5/5!+…+x^2n+1/(2n+1)! +o(x^2n+1)

Question 12

DL (1+x)ª

Answer 12

1+ax+(a(a-1)/2!)x²+…+(a(a-1)…(a-n+1)/n!)x^n +o(x^n)