Midterm 3 Flashcards
(29 cards)
Intermediate Value Theorem
If f is continuous on the interval [a,b] and M is a number between f(a) and f(b),
then there’s at least one number c in the interval (a,b) such that: f(c)=M
Mean Value Theorem
If f is continuous on [a,b] and differentiable on
(a,b),
then there’s at least one point c in (a,b) such that:
f’(c)= f(b) - f(a) / b-a
(slope of secant line = slope of tangent line)
Rolle’s Theorem
If f is continuous on [a,b] and differentiable on (a,b) with f(a)=f(b),
then there’s at least one point c in (a,b) such that:
f’(c)=0
Linear Approximation Formula
f(x) ~ L(x)= f(a) + f’(a)(x-a)
Error for Linear Approximations
Absolute value of (approximated value - real value)
f’(x)=
dy/dx
dx=
change in x
dy=
f’(x) dx
change in y=
f(x+dx) - f(x)
Can area be zero?
YES
Area of Trapezoid
A= (a+b)(h) / 2
Surface Area/Volume of Cone
SA= (pi)(r^2) + (pi)(r)(s) s= slant V= (pi)(r^2)(h) / 3
Surface Area/Volume of Sphere
SA= (4)(pi)(r^2) V= (4/3)(pi)(r^3)
F’(x)=
f(x)
A log of a limit=
a limit of a log!
d/dx [ f(g(x)) ] =
f’(g(x)) * g’(x)
change in x=
b-a / n
x sub k=
a + k(delta x)
Exact (net) Area=
the limit as n goes to infinity of:
sigma (k=1 to n) of f(x sub k *)(delta x)
Sum formula of c=
cn
Sum formula of k=
n(n+1) / 2
Sum formula of k^2=
n(n+1)(2n+1) / 6
Sum formula of k^3=
n^2(n+1)^2 / 4
Even Function
f(-x) = f(x)
