# Calc 250 FINAL

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valleystudent84's
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2015-12-17 13:03

## Section

Question | Answer |
---|---|

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? resuts | substitute 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? results | substitute your extrema into your 2nd Dx - Tells you if the extrema are max or mins (don't have to bee either) |

Critical munbers | Any value that makes the 1st Dx 0 or undefined. |

Three different Horizontal asymptotes | n/n^2 is Y=0 - n/n = ratio of the two - n^2/n = Oblique Asm. or hole |

Conditions for Rolies theorom | I. 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 theorom | I. Continuous on closed interval - II. Must be differentiable on the open interval |

Concavity - Define | here f"(x) is pos = Concavity up, where concavity is neg = concvity down. |

point of inflection | Any point where the concavity changes |

Definition of a Limit process | I. 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 Process | I. f(c) DOES EXIST - II. Lim at the pt DOES EXIST - III. Lim MUST = func value |

Intermediate Value theorem Pocess | I. 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 x | 1 |

Dx Power Rule | DxX^n-1 |

Dx Product Rule | Dxf(x)*g(x) = f'(x)*g(x)+f(x)*g'(x) |

Dx Quotient Rule | Dx f(x)/g(x) = g(x)*f'(x)-f(x)*g'(x)/(g(x))^2 |

Dx Chain Rule | Dx F(G(x)) = F'(G(x))*G'(x) |

Trig Dx are ALWAYS _ rule | Chain rule!!! |

Setting up for Optimization problems | I. 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 Calculus | ʃ [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)^n | a^(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 sphere | 4(pi)(r)^2 |

Volume of a sphere | 4/3(Pi)(r)^3 |

Volume of a cone | 1/3(Pi)(r)^2(h) |

Volume of a cube | a^3 |

Surface area of a cube | a^6 |

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