1 x sqrt x 4

    • [PDF File]InteractiveMatlabCourse - University of Notre Dame

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      Table 1.1: Standard operations MATLAB Standard sin(x) sin(x) sqrt(x) √ x cos(x) cos(x) exp(x) ex tan(x) tan(x) log(x) ln(x) asin(x) sin−1(x) log10(x) log 10(x) acos(x) cos−1(x) abs(x) |x| atan(x) tan−1(x) sign(x) sign(x) mean(x) mean(x) std(x) standard deviation min(x) min(x) max(x) max(x) rand(x,y) returns x×y array of random numbers ...

    • [PDF File]Volumes by Cylindrical Shells: the Shell Method

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      Ex. Find the volume of the solid generated by revolving the region bounded by y = x2, y = 0, x = −1, and x = 1, about the line x = 2. The axis of rotation, x = 2, is a line parallel to the y-axis, therefore, the

    • [PDF File]TRIGONOMETRY LAWS AND IDENTITIES

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      1 1 y =sin(x) x y ⇡ 2 ⇡ 3⇡ 2 2⇡ 1 1 y = cos(x) x y ⇡ 2 ⇡ 3⇡ 2 2⇡ 1 1 y = tan(x) x y 0 30 60 90 120 150 180 210 240 270 300 330 360 135 45 225 315 ⇡ 6 ⇡ 4 ⇡ 3 ⇡ 2 2 3 3 5 ⇡ 7⇡ 6 5⇡ 4 4⇡ 3 3⇡ 2 5⇡ 3 7⇡ 4 11⇡ 6 2⇡ ⇣p 3 2, 1 ⌘ ⇣p 2 2, p 2 ⌘ ⇣ 1 2, p 3 2 ⌘ ⇣ p 3 1 ⌘ ⇣ p 2 p 2 ⌘ ⇣ 1, p 3 ...

    • [PDF File]Data Flow Graphs

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      x 2 4 2 1 − + − = a ac b b x 2 4 2 2 ... -1 +-x / ** sqrt x x b4ca 2-/ X 1 X 2 T 2 2 1 1 1 67 8 +/-*// ** sqrt-1 1 2 1 1 1 1 1 1 1 1. Resource Constraints Resource is given, minimize the long time List based scheduling ...

    • [PDF File]Techniques of Integration - Whitman College

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      cos(4) + 1 2 cos(2). A somewhat clumsy, but acceptable, alternative is something like this: Z4 2 xsin(x2)dx = Z x=4 x =2 1 2 sinudu = − 1 2 cos(u) x =4 x = − 1 2 cos(x2) 4 = − cos(16) 2 + cos(4) 2. EXAMPLE 8.1.4 Evaluate Z1/2 1/4 cos(πt) sin2(πt) dt. Let u = sin( πt) so du = πcos( ) or du/π = cos(πt)dt. We change the limits to sin ...

    • [PDF File]Chapter 1 Iteration - MathWorks

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      x = sqrt(1 + x) takes the current value of x, computes sqrt(1 + x), and stores the result back in x. In mathematics, the equals sign has a different meaning. x = √ 1+x is an equation. A solution to such an equation is known as a xed point. (Be careful not to confuse the mathematical usage of xed point with the computer arithmetic usage of ...

    • [PDF File]18.06 Problem Set 6 - Solutions - MIT

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      (3) Apply the Gram-Schmidt algorithm to the set {1,x,x2} to obtain an orthonormal basis {f 0,f 1,f 2} of all degree-2 polynomials. Solution Denote g 0 = 1,g 1 = x and g 2 = x2. We begin by letting G 0 = g 0 = 1. For G 1: G 1 = g 1 − hG 0,g 1i hG 0,G 0i G 0 = x− R 1 0 xdx R 1 0

    • Finding the Equation of a Tangent Line

      1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

    • [PDF File]Trigonometric Substitutions Math 121 Calculus II

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      Since the derivative of f(x) = 1 2 x2 is x, the length is L= Z 1 0 p 1 + x2 dx: We’ll use the trig sub of the second kind with x= tan , dx= sec2 d , and p 1 + x2 = sec . Then the integral becomes L= Z ˇ=4 0 sec3 d : It takes an application of integration by parts to nd that an antiderivative of sec3 is 1 2 sec tan + 1 2 ln j+ tan . Given ...

    • [PDF File]Table of Integrals - UMD

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      ©2005 BE Shapiro Page 3 This document may not be reproduced, posted or published without permission. The copyright holder makes no representation about the accuracy, correctness, or

    • [PDF File]7.2 Finding Volume using the Washer Method

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      3 7.2 Finding Volume using the Washer Method Example 1) Find the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x2 about the x-axis.

    • [PDF File]2003 AP Calculus BC Scoring Guidelines - College Board

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      4 2 0 5 1 3 ¨ + yydy ¦ = 0.346 or 0.347 3 : 1 : limits 1 : integrand 1 : answer £¦ ¦¦ ¦ ¤ ¦¦ ¦¦ ¦¥ (c) xr= cosR; yr= sinR 22 22 22xy r r = 1cos sin 1º RR= 2 22 1 cos sin r RR = 2 : 22 2 1 : substitutes cos and sin into 1 1 : isolates xr yr x y r R R £¦¦ = ¦¦ ¦¦¤ = = ¦¦ ¦¦ ¦¥ (d) Let C be the angle that segment OP ...

    • [PDF File]Math 241 Homework 12 Solutions

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      semicircle y =-2 1 - x 2 to the semicircle y = 2 1 - x . 5. The base of a solid is the region between the curve y = 22 sin x and the interval 30, p 4 on the x-axis. The cross-sections perpen-dicular to the x-axis are a. equilateral triangles with bases running from the x-axis to the

    • [PDF File]Integration by substitution

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      Now, in this example, because u = x + 4 it follows immediately that du dx = 1 and so du = dx. So, substituting both for x+4 and for dx in Equation (1) we have Z (x+4)5 dx = Z u5du The resulting integral can be evaluated immediately to give u6 6 +c. We can revert to an expression

    • [PDF File]Math 104: Improper Integrals (With Solutions)

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      x= 1, so we need to split the problem into two integrals. Z 3 0 1 (x− 1)2/ 3 dx= Z 1 0 1 (x− 1)2/ dx+ Z 3 1 1 (x− 1)2/3 dx. RyanBlair (UPenn) Math104: ImproperIntegrals TuesdayMarch12,2013 11/15. ImproperIntegrals Example 5 Find Z 3 0 1 (x−1)2/3 dx, if it converges. Solution: We might think just to do Z 3 0 1

    • [PDF File]Does it converge or diverge? If it converges, find its ...

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      1 x2(x−1) dx = 1 x + 1 2 ln(x−1)− 1 2 ln(x+1) 4. Z ∞ 1 1 1+ex dx Use u = 1+e x, so du = e dx, so that du = (u−1)dx. Substitution gives: Z 1 u(u−1) du = Z −1 u + 1 u−1 du Antidifferentiate, and we get: −ln(1+ex)+ln(ex) = ln ex 1+ex Take the appropriate limit to get an answer of ln(2) 5. Z ∞ 0 dx (x+1)2(x+2) dx Use partial ...

    • [PDF File]INTERPOLATION - University of Iowa

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      x0 =0,x1 = π 4,x2 = π 2 and yi=cosxi,i=0,1,2 This gives us the three points (0,1), µ π 4, 1 sqrt(2) ¶, ³ π 2,0 ´ Now find a quadratic polynomial p(x)=a0 + a1x+ a2x2 for which p(xi)=yi,i=0,1,2 The graph of this polynomial is shown on the accom-panying graph. We later give an explicit formula.

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