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Ms. Bertsos knows the rate a population of bacteria is increasing ... 'Pulling out a konstant' Some General Rules. Differentiation Formula Integration Formula ...
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Use the integral to convert dy/dx to y = f(x) ... A $20,000 art collection is increases in. value at a rate of 300t dollars per year ...
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Antiderivatives. Definition. A function F is an antiderivative of f on an interval ... of f on I, then G is also an antiderivative of f on I if and only if ...
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A function F is the Antiderivative of f if ... Find all functions g such that: NOTE: see pg. 250 for more Antiderivative Rules Ex 3: Evaluate Ex 4: ...
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tan x. ax / ln a. ax. sin x. cos x. ex. ex - cos x. sin x. ln |x| xr 1/(r 1) xr, r -1. Antiderivative ... Mika Sepp l : Antiderivatives ...
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6 Integration Antiderivatives and the Rules of Integration Integration by Substitution Area and the Definite Integral The Fundamental Theorem of Calculus
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4.1 Antiderivatives and Indefinite Integration 4.1 Antiderivatives and Indefinite Integration 4.1 Antiderivatives and Indefinite Integration 4.1 Antiderivatives and ...
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The antiderivative of a function f is a function F such that F'=f. ... Solution: Differentiate the functions: ... Antiderivative of Power Function: ...
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k(x) = sec2(x) K(x) = tan(x) C. because K'(x) = k(x) Differential Equation ... Basic Integration Rules. Note the inverse nature of integration and differentiation ...
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To solve an initial value problem. Find the general solutions for antiderivatives ... Algebra Rules. 3) Algebra Rules. Sum rule. Difference Rule. Constant ...
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Just as represents finding a derivative, the ... Find the equation for y, given the derivative and. the indicated point on the curve. ...
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We begin with two examples. Find any function whose derivative is f(x) = 9x2+4x b) f(x)=3cos2x. These are the antiderivatives. An antiderivative of the ...
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... the concept of an antiderivative Understand the geometry of the antiderivative and that of slope fields Work rectilinear motion ... 12 Motion Problems ...
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Consider the function whose derivative is given by. ... Notice that we say is an antiderivative and not the antiderivative. Why? ... HippoCampus. Slope Fields ...
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... given by the FTC between antiderivatives and integrals, the ... (one antiderivative for each value of the constant C). INDEFINITE VS. DEFINITE INTEGRALS ...
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4.1: Antiderivatives and Indefinite Integration (Part II) Greg Kelly, Hanford High School, Richland, Washington Objectives Write the general solution of a ...
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5.3 Definite Integrals and Antiderivatives Greg Kelly, Hanford High School, Richland, Washington Page 269 gives rules for working with integrals, the most important ...
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6.3 Integration by Parts & Tabular Integration Problem: Integrate Antiderivative is not obvious U-substitution does not work We must have another method to at least ...
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Numerical Integration Approximating Definite Integral The Trapezoidal Rule Some elementary functions do not have antiderivatives that are elementary functions.
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Numerical Integration Approximating Definite Integral The Trapezoidal Rule Some elementary functions do not have antiderivatives that are elementary functions.
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Slope Fields and Euler s Method When taking an antiderivative that is not dealing with a definite integral, be sure to add the constant at the end.
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Derivatives What do we mean by the derivative of a function f (x) at a point (a, f (a ... Limits Derivatives Recall Some Derivative Facts Antiderivatives Recall (?)
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Going back to the function f(x) = x2, we see that the general antiderivative. of f is ?x3 C. ... f(x) = xn, n 0. f(x) = x-3. Example 1. ANTIDERIVATIVES. If F ...
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Integral calculus: areas and volumes. antiderivatives. 13. Differential Calculus Review ... Solid integral across shape. See Mirtich,Eberly for more details ...
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Apply concepts of indefinite integrals to a real world ... dx which is similar to rules we have seen ... be used to find an antiderivative that is not ...
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The Fundamental Theorem of Calculus. If a function f is continuous on the closed interval [a,b] and F is an antiderivative of f on the interval [a,b], then
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Index A - C A Absolute Value Alternating Series Antiderivative Arc Length Functions Arccos Arcsin Arctan Area of a Domain under the Graph of a Function
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Riemann Sums and The Definite ... clarification regarding INDEFINITE INTEGRALS (with which we have worked before in finding antiderivatives) and DEFINITE INTEGRALS ...
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Fundamental Theorem of Calculus Part 2 Thurs Feb 5 Do Now Evaluate each definite integral 1) 2) Part 1 Review FTC Part 1 stated that we can use antiderivatives to ...
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This gives us antiderivatives (integrals) of these functions ... Application. Find the area enclosed by. x = 1/2, x = 2, y = 0, and. Which pattern does this match? ...
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Section 7.2. Integration by Parts. Consider the function. Use substitution to find the antiderivative. Let u = x2, u' = 2 x. Consider the function ...
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indefinite integral of f, and we introduce the. notation ... NOTE to find the indefinite integral is the. same as to find the most general antiderivative ...
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Most computer mathematics systems abuse this notation for ... An odometer in a car is an antiderivative of the tachometer, but we do not have odometer readings. ...
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Calculus B L98 Fundamental Theorem of. Calculus, Part 2, The. Natural Logarithm Function ... Part1: where F is any antiderivative of f. Part2: Definition of lnx: ...
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Trig Identities and Applications A calc student upset as could be That his antiderivative didn't agree With the one in the book E'en aft one more look.
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... column under I in a similar fashion except you will write an antiderivative of ... The table of integrals then shows how to write the answer to that example. ...
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An example is the function sin(x)/x. It is not possible to analytically find its antiderivative ... use Si all the time. Optics, harmonic motion and ...
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The daily cost to manufacture x items is C = 5000 25x 2. How many items should ... minimize the daily. average cost. 4.10 Old problem. Given a function, find ...
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... Example Find the following derivatives Section 6.4 Second Fundamental Theorem of Calculus The 1st Fundamental Theorem of ... Document presentation format: On ...
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Calculus 5.5 Subject: Trapezoidal Rule Last modified by: Michelle Honeycutt Company: Hanford High School ...
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Title: Section 7.2* Author: Allen Fuller Last modified by: z Created Date: 6/20/2005 1:40:46 AM Document presentation format: On-screen Show (4:3) Other titles
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We adopt the convention that, when a formula for ... We are guided by the fact that the slope of. y = F(x) is f (x). Graph Example 5 ...
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5.5 Numerical Integration. Mt. Shasta, California. Greg Kelly, Hanford High School, ... Using integrals to find area works extremely well as long as we can find the ...
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Title: Calculus 4.2 Subject: Mean Value Theorem Author: Gregory Kelly Last modified by: Gregory Kelly Created Date: 10/17/2002 4:22:00 AM Document presentation format
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Definite Integrals Finding areas using ... Definite Integrals Finding areas using the Fundamental Theorem of Calculus The Definite Integral ... Document presentation ...
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Mean Value Theorem for Derivatives 4.2 Teddy Roosevelt National Park, North Dakota If f (x) is a differentiable function over [a,b], then at some point c between a ...
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Radius of Convergence Let be a power series. The set of x for which S(x) converges is an interval centered at x0; endpoints may or may ...
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If the graph of flies above the graph of g, from a to b, then the area of the ... Similarly, if f and g are two continuous rate-of-change functions, then the ...
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Use your graphing calculator to graph the integrand. and determine whether the integral is... with your calculator. Enter the function in y =. GRAPH & CALC ...
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Title: Calculus 6.2 Subject: Integration by Substitution & Separable Differential Equations Author: Gregory Kelly Last modified by: Mike Efram Created Date
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A car-leasing firm must decide how much to charge for maintenance on the cars it ... What total maintenance cost can the company expect for a 2-year lease? ...
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... integration C inside F(x) reflects the fact that the boundary B may be chosen differently. Corollary: the area under the curve between the verticals x=B and ...
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Write an equation for the quantity that is to be optimized. ... piece of cardboard by cutting congruent squares from the corners and folding up the sides. ...
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The Fundamental Theorem of Calculus ... Document presentation format: ... Times New Roman Arial Calibri Default Design Microsoft Equation 3.0 Section 4.3 A ...
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One technique is to inject a dye into a main vein near the. Heart. ... Definite Integral and Area. If an integrable function y = f(x) is nonpositive, the nonzero ...
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What does this have to do with automorphic forms? f'(x) is essentially the q-function ... Regularity of Automorphic Distributions ...
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