Calculus

  1. Taylor:Taylor
    • series(cos(x),x,0,5) >>>1-x22+x424+O(x5)

  2. Gamma:Γ(x)=0tx-1etdt,x>0
    • gamma(1) >>>1

  3. Zeta:ζ(s)=lim(1+12s+13s+14s...+1ns)
    • zeta(2) >>>1.64493406684823

  4. Limit:
    • limit(sin(x)/x,x,0) >>>1

  5. Right limit:
    • limit(1/x,x,0,'+') >>>oo

  6. Left limit:
    • limit(1/x,x,0,'-') >>>-oo

  7. Indefinite integral:
    • xdx >>>0.5*x2

    • integrate(x,x) >>>0.5*x2

  8. Definite integral:
    • integrate(pow(e,-x),x,0,inf) >>>1

  9. Multiple integral

    Repeat the corresponding integral operation.

  10. N-th order derivative:
    • y=ln(x) y'(x) >>>x-1

    • y=ln(x) y'' >>>-1x2

    • (ln(x))' >>>x-1

    • d/dx(ln(x)) >>>x-1

    • diff(ln(x),x,2) >>>-1x2

  11. N-th order partial derivative:
    • (y*ln(x))''(x) >>>-yx2

    • d/dy(y*ln(x)) >>>ln(x)

    • diff(y*ln(x),x,2) >>>-yx2