Do you know your dx trigs/hypers
what are the dx's of the 6 main functions
sin x -> cosx
cosx -> -sinx
tanx -> sec^2 x
cscx -> -cscxcotx
secx -> secxtanx
cotx -> -csc^2 x
What is the Taylor polynomial formula
T_n(x) =sum_(k=0)^n (f^(k)(a))/(k!)(x-a)^k
What is L'Hôpital's rule
lim_(x->c)f(x)/g(x) = lim_(x->c)(f'(x))/(g'(x)
What are the dx's of the inverse of the 6 main functions
sin^-1 x-> 1/sqrt(1-x^2)
cos^-1 x -> -1/sqrt(1-x^2)
tan^-1 x -> 1/(1+x^2
cot^-1 x -> -1/(1+x^2
sec^-1 x -> 1/(|x|sqrt(x^2 -1)
csc^-1 x -> -1/(|x|sqrt(x^2 -1)
What is the linear approximation formula
L(x)=f(a)+f'(a)*(x-a)
What is the formula for the exponential indeterminate form
lim_(x->a)f(x)^g(x) =e^(lim_(x->a)g(x)ln(f(x))
What are the dx's of the hyperbolic functions
sinh x -> cosh x
cosh x -> sinh x
tanh x -> sec^2h (x)
coth x -> -csc^2h x
sech x -> -sechxtanhx
csch x -> -cschxcothx
What does Δy equal
f(x+Δx)-f(x)
What are the indeterminate forms
1^(±oo),±oo^0,0^0,0/0,(±oo)/(±oo),0*±oo,oo-oo
What are the dx's of the inverse of the hyperbolic functions
sinh^-1(x) -> 1/sqrt(1+x^2
cosh^-1(x) -> 1/sqrt(x^2-1
tanh^-1(x)-> 1/(1-x^2)
csch^-1(x) -> -1/(|x|sqrt(x^2+1)
sech^-1(x) -> -1/(|x|sqrt(1-x^2)
coth^-1(x) -> 1/(1-x^2
What is the mean slope formula
(f(b)-f(a))/(b-a
lim_(d->oo)sqrt(d^2+6d+5)-sqrt(d^2-2d+9
=4
What are the true forms of sinh and cosh
sinhx= (e^x-e^-x)/2
coshx= (e^x+e^-x)/2
What is Newton's method
x_(n+1)=x_n-(f(x_n))/(f'(x_n)
lim_(x->0^+)(1+3x)^(2/x)
=e6