Theorems
If function is continuous on [a,b] then f must attain absolute maximum and minimum once
What is Extreme Value Theorem?
d/dx of xn
What is nxn-1?
Integral of 0dx
f''(x) < 0
What is concave down?
d/dx(ex)
What is ex * x'?
If a(x) <= f(x) <= g(x) for all numbers and at some point where x=k where a(k) = g(k), then f(k) must be equal at a(k) and g(k).
What is squeeze theorem?
Derivative of sin(u)
What is cos(u)*u'?
Integral of ex
What is ex + c?
f'(x) = 0 or does not exist
What is critical point?
limx->a f(x+h)-f(x) / h
What is the Definition of a Derivative?
If f(x) continuous on [a,b], let M be between f(a) and f(b). Then there exists a point c where a < c < b and f(c) = M.
What is Intermediate Value Theorem?
d/dx ( ln(u) )
What is 1/u * du/dx?
Anti-derivative of xn?
What is (xn+1 / (n+1) ) + c?
point where a function changes continuity
integral from a to a of f(x)
What is 0?
If f and F continuous on [a,b] and F'(x)=f(x), then the integral from a to b of f(x)dx = F(x)]ba = F(b)-F(a).
d/dx ( cot (u) )
What is -csc2(u)*u'?
Anti-derivative of csc2(x)dx
What is -cot(x)+c?
limx->a-
What is x approaches a from the left?
integral from a to b of |v(t)| represents
what is distance?
If f is continuous on [a,b], there exists a number c where the integral from a to b of f(x)dx = f(c)(b-a)
What is Mean Value Theorem for Integrals?
d/dx( sin-1(x) )
What is ( 1/sqrt(1-x2) ) * x'?
Anti-derivative of du / a2+u2
What is 1/a * tan-1(u/a) + c?
limit x->a f(x) exists
f(a) exists
limit x->a f(x) = f(a)
What is definition of continuity?
Formula for Washer Method
What is pi * integral of a to b of (R2-r2)