# Calc 250 FINAL

version from 2015-12-17 13:03

## Section

sinθ/θ =1
1-cosθ/θ = 0
Σi = n(n+1)/2
Σi^2 =n(n+1)(2n+1)/6
Σi^3 = n^2(n+1)^2/4
Σ constant(Constant)n
Original Func tells us (4) f`(x) - intercepts - asymptotes - all points on graph
f`(x) tells us (5)f"(x) - critical numbers - extrema - increasing and decreasing - 1st Dx test
f"(x) tells us (3)Concavity - Pt.s of inflection - 2nd Dx Test
What is the 1st Dx test? resutssubstitute points BETWEEN your extrema into your 1st Dx - tells you if your extrema are increasing or decreasing (don't have to be either)
What is the 2nd Dx test? resultssubstitute your extrema into your 2nd Dx - Tells you if the extrema are max or mins (don't have to bee either)
Critical munbersAny value that makes the 1st Dx 0 or undefined.
Three different Horizontal asymptotesn/n^2 is Y=0 - n/n = ratio of the two - n^2/n = Oblique Asm. or hole
Conditions for Rolies theoromI. Func MUST be continuous on closed interval - II. Must be differentiable over the OPEN interval - III. If f(A) = f(B) there exists an f(c) that is a critical number
Conditions for Mean Value theoromI. Continuous on closed interval - II. Must be differentiable on the open interval
Concavity - Definehere f"(x) is pos = Concavity up, where concavity is neg = concvity down.
point of inflectionAny point where the concavity changes
Definition of a Limit processI. Find L by subbing given number into func - II. put func minus L into ABS and set < E - IIII. Solve for E and make sure that the func is minus something and in ABS - IV. Chooose _ < or = lower E
Continuity at a point ProcessI. f(c) DOES EXIST - II. Lim at the pt DOES EXIST - III. Lim MUST = func value
Intermediate Value theorem PocessI. Func IS continuous on closed interval and f(a) DOES NOT = f(b) - II. k is a number BETWEEN those two x values - III. DOES NOT APPLY TO ANYTHING OTHER THAN A POLYMONIAL
Dx of x1
Dx Power RuleDxX^n-1
Dx Product RuleDxf(x)*g(x) = f'(x)*g(x)+f(x)*g'(x)
Dx Quotient RuleDx f(x)/g(x) = g(x)*f'(x)-f(x)*g'(x)/(g(x))^2
Dx Chain RuleDx F(G(x)) = F'(G(x))*G'(x)
Trig Dx are ALWAYS _ ruleChain rule!!!
Setting up for Optimization problemsI. Identify formula that the problem is dealing with - II. Dx with respect to time - III. Everything is the chain rule - IV. Identify the info given
Whenever doing ʃ without limits add _+ c
ʃ(x^n)dx = (x^n+1)/(n+1)
ʃe^x = ('X)e^x
Fundamental theorem of Calculusʃ [with limits A and B] f(x)dx = ʃf(B) - ʃf(A)
ʃ(du/U) = lnABS(U) + C
Dx lnABS(U) =(1/U)(U')
a^(m) * a^(n)a^(m+n)
a^(m) / a^(n)a^(m-n)
(a^m)^na^(m*n)
a^(m)*b^(m)a^(m*m)
a^(m)/b^(m)(a/b)^m
Area of a circle(Pi)(r)^2
Surface Area of a sphere4(pi)(r)^2
Volume of a sphere4/3(Pi)(r)^3
Volume of a cone1/3(Pi)(r)^2(h)
Volume of a cubea^3
Surface area of a cubea^6