Know Cold Flashcards
memorize
limits: vertical asymptote (x=c)
lim f(x) = +/-infinity
x–>c
horizontal asymptote (y=L)
lim f(x) = L
x–> +/-infinity
L’Hospital
f(c)/g(c) = 0/0 or infinity/infinity then lim f(x)/g(x) = lim f’(x)/g’(x)
x–> c
When is a function continuous?
f(c) is defined
lim(-) f(x) = lim(+) f(x)
lim f(c) = f(c)
x–> c
d/dx[C]
0
d/dx[sin(x)]
cos(x)
d/dx[cos(x)]
-sin(x)
d/dx[tan(x)]
sec^2(x)
d/dx[sec(x)]
sec(x)tan(x)
d/dx[e^x]
e^x
d/dx[a^x]
ln(a)a^x
d/dx[ln(x)]
1/x
d/dx[cot(x)]
-csc^2(x)
d/dx[csc(x)]
-csc(x)cot(x)
d/dx[x^(n-1)]
nx^(n-1)
IVT
if f(x) is continuous on the the interval [a,b] and Y is between f(a) and f(b) there exist a c value within [a,b] where f(c) = Y exists
MVT
if f(x) is continuous on [a,b] and differentiable on (a,b) then there exists some C value within (a,b) such that f’(c) = f(b)-f(a)/b-a
EVT
if f(x) is continuous on [a,b] then f(x) has an absolute maximum and absolute minimum on [a,b]
total distance traveled
integral of the absoulte value of v(t)
displacement
integral of v(t)
volume of solids (cross sections) - square
integral S^2
volume of solids (cross sections) - rectangles
integral B * H
volume of solids (cross sections) - isosceles right leg
1/2 integral L^2
volume of solids (cross sections) - isosceles right hypotenuse
1/4 integral H^2
