##### More Calculus final formulas
1 / 43
Term:
Definition:
Show example sentence
Show hint

#### Complete List of Terms and Definitions for More Calculus final formulas

Terms Definitions
∫tanx -ln|cosx|+C
tanh^-1(x) (1/2)ln[(1+x)/(1-x)]
sinh(-x) -sinh(x)
d/dx cosx -sinx
d/dx secx secxtanx
m = slope
d/dx(tan^-1 x) 1/(1+x^2)
d/dx(coth x) -csch^2(x)
d/dx(cos^-1 x) -1/√(1-x^2)
Marginal Cost C'(q)
∫secx ln|secx+tanx| + C
volume of cone 1/3πr^2h
d/dx lnu 1/u du/dx
cosh(x+y) cosh(x)*cosh(y) + sinh(x)*sinh(y)
Revenue price x quantity
Area of trapezoid 1/2 (b1+b2)(h)
d/dx sinh x cosh x
d/dx(tanh^-1 x) 1/(1 - x^2)
cosh x (e^x + e^-x)/2
sinh x (e^x - e^-x)/2
optimization minimum or maximum problem
critical point local minimum or maximum
cosh^-1(x) ln[x + √(x^2 - 1)]
essential discontinuity curve has a vertical asymptote
L'hopital's rule lim (x->c) f(x)/g(x) = f'(x)/g'(x)
only for indeterminate functions (equal 0/0 or ∞/∞)
so basically solve them separately
cosh x e^x + e^-x / 2
jump discontinuity curve "breaks: and starts somewhere else
(left limit doesn't equal right limit)
Profit Revenue - cost usually written as pi
sigma notation definite integral
number at the top tells the number of intervals
number at the bottom tells where to begin
y=e^i(x-a)^2 a shifts the graph left or right divide (x-a)^2 by b and b makes the graph wider or narrower
y=e^i(x-a)^2 a shifts the graph left or right
divide (x-a)^2 by b and b makes the graph wider or narrower
trapezoid rule b-a/2n [f(xo) + 2f(x1) + 2f(x2) ... f(xn)}
average value 1/b-a integral from b to a f(x) dx
y=a(1-e^-bx) a is the asymptote and b is the stretch or shrink of the graph
delta t b-a/n
n is the number of intervals and b and a is the interval
y=a(x-h)^2 + k a is stretch or shrinkh shifts right and leftb shifts up and down
slope of a line = y2 - y1 / x2 -x1
y=a(x-h)^2 + k a is stretch or shrink
h shifts right and left
b shifts up and down
hyperbolic functions to know cosh(0) = 1sinh(0) = 0cosh(-x) = cosh x sinh (-x) = -sinh x cosh^2 x - sinh^2 x = 1
Extreme Value theorem if f is continuous then must have a global max and global min on the closed interval
A function is a relation in which each element of the domain (x value - independent variable ) is paired with only one element of the range ( y value - dependent variable )
A function is A relation can be tested to see if it is a function by the vertical line test. Draw a vertical line through any graph, and if it hits an x-value more than once, it is not a function.
equation of a line y - y₁ = m ( x - x1 )