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AP Calc BC
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Term | Definition |
---|---|
e^x | 1+x+(x^2)/2!+(x^3)/3!+(x^4)/4!+...+(x^n)/n!+(e^Zn)(x)^(n+1)/(n+1)! |
1/(1+x) | 1-x+(x^2)-(x^3)+(x^4)-(x^5)+..... |
sin(x) | x-(x^3)/3!+(x^5)/5!-(x^7)/7!+(x^9)/9!+......+ |
cos(x) | 1-(x^2)/(2!) +(x^4)/(4!)-(x^6)/(6!)+....+term in x^n+[+/-sin(Zn) or +/-cos(Zn)](x)^(n+1)/(n+1)! |
e^x (general form) | Σ(x^n)/ (n!) n=0 to infinity |
1/(1+x) (general form) | Σ(-1)^n x^n , for |x| < 1 n=0 to infinity |
sin(x) (general form) | Σ(-1)^n x^2n+1/(2n+1)! , for all real x n=0 to infinity |
cos(x) (general form) | Σ(-1)^n x^2n/(2n)! , for all real x n=0 to infinity |