Derivatives
Find the derivative of:
2x^3
What is
6x^2
Evaluate
int cos x dx
What is
sin x + C
Find the limit:
lim_(x->-3) |x+3|
What is 0
The first four terms of the series:
1/(1-x)
What is
1+x+x^2+x^3
If f is cont. on interval [a,b] and differentiable on (a,b), then there exists c on the interval such that
(f(b)-f(a))/(b-a)=f'(c)
What is Mean Value Theorem
The derivative of
cos(5x^2)
What is
-10x sin(5x^2)
Find
int x^n dx
in terms of n
What is
(x^(n+1))/(n+1) + C
Find the limit:
lim_(x->-1) (x^2 + 3x + 2)/(x+1)
What is 1
The first four terms of the series:
cos x
What is
1-x^2/(2!)+x^4/(4!)-x^6/(6!)
Definition: The limit, L, of a function, f(x), as x approaches a exists iff
lim_(x->a-) f(x) = lim_(x->a+) f(x) = L
What is a Limit
Calculate the derivate of:
3(sinx/cosx)
What is
3sec^2 x
Evaluate
int cosx cos(sinx) dx
What is
sin(sinx)+C
Find the limit:
lim_(x->oo) (3x^7-5x^3+2)/(6x^7 +4x^4-3x)
What is 1/2
The first four terms of the series:
cos(x^2)
What is
1-(x^4)/(2!)+(x^8)/(4!)-(x^12)/(6!)
The type of integrals in which the function contains a vertical asymptote or undefined value on the interval, requiring the use of limit to evaluate the integral.
What is Improper Integrals
Calculate f' in terms of g' for
f(x)=x^2*g(x)
What is
x^2*g'(x)+2xg(x)
Evaluate
int cos x e^sinx dx
What is
e^sinx +C
lim_(x->0) tan(pix)/(ln(1+x))
What is
pi
The first four terms of the series:
1/(1+x^3)
What is
1-x^3+x^6-x^9
Estimates a function value using small increment or steps when the differential equation cannot be solved
What is Euler's Method
Calculate y' for
x^2 + sin y = xy
What is
(y-2x)/(cos y - x)
Evaluate
int x sin(3x^2) dx
What is
-cos(3x^2)/6+C
lim_(h->0) (sin^2(x+h)-sin^2x)/h
lim┬(h→0) (sin^2(x+h)-sin^2x)/h
What is
2 sinx cosx
The first four terms of the series:
2 sin(-x)
What is
-2x + (2x^3)/(3!)-(2x^5)/(5!)+(-2x^7)/(7!)
The formula
int_(theta_1)^(theta_2) 1/2(r(theta)^2) d theta
What is Area of Polar Curve