Plot y = x 2 and y = (x1) 2 1 syms x y y = x^2;% x=a,a∆x, a2∆x, a3∆x, , b % that is, vector from a to b in increments of size ∆xView Notes Exam2 from MATH 550 at University of Notre Dame 1(6pts) Find dz/dt when t = 0, where z = x2 y 2 2xy , x = ln(t 1) and y = e3t (a) 8 (b) 2 (c) 1 (d) 6 (e) 5 Solution Notice
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(a) u(x,y) = x2 y2;To graph a square root function, we can plugin numbers in the place of the variable 'x' and find the function or the 'y' value for those numbers and plot the points on the plane Example 1 Graph the square root function, y = √x352 Chapter 14 Partial Differentiation k;
X diverges to infinity, so does A, by the comparison test Problem 27 (a) If a > 0, find the area of the surface generated by rotating the loop of the curve 3ay2 = x(a−x)2 about the xaxis (b) Find the surface area if the loop is rotated about the yaxis Solution1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to yH = cos(x) cos(2*x);
94 7 Metric Spaces Then d is a metric on R Nearly all the concepts we discuss for metric spaces are natural generalizations of the corresponding concepts for R with this absolutevalue metric Example 74 Define d R2 ×R2 → R by d(x,y) = √ (x1 −y1)2 (x2 −y2)2 x = (x1,x2), y = (y1,y2)Then d is a metric on R2, called the Euclidean, or ℓ2, metricIt corresponds toA polynomial in x, P (x), is an expression containing only nonnegative, whole number powers of x In the polynomial equation P (x) = 13x2 − x 1 X is the variable 13 is the coefficient of x2 and 13x2 is the quadratic term −1 is the coefficient of x and −x is the linear term The constant term is 1 The degree of the polynomial is 2Figure 2 Part of the region S bounded by x2z2 = a2 and x2 y2 = a2 for x ≥ 0 Note that the projection of region S1 on the y − z plane, call it R is a a square 0 ≤ y ≤ a, 0 ≤ z ≤ a We break
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In this tutorial we shall derive the integration of the square root of a^2x^2, and solve this integration with the help of the integration by parts methods The integral of a 2 – x 2 is of the form I = ∫ a 2 – x 2 d x = x a 2 – x 2 2 a 2 2 sin – 1 ( x a) c This integral can be written as I = ∫ a 2 – x 2 ⋅ 1 d xIn general this is called a level set; Plot the vector field F(x, y, z) = x p x 2 y 2 i y p x 2 y 2 j and the parabola y = 1 x 2 Use the graph to determine whether the integral Z C F dr will be positive or negative or zero along the parabola from (1, 2) to (1, 2)
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The base radical function, y= √ __ x Graph Radical Functions Using Tables of Values Use a table of values to sketch the graph of each function Then, state the domain and range of each function a) y = √ __ x b) y = √ _____ x 2 c) y = √ __ x 3 Solution a) For the function y= √ __ x , the radicand x must be greater than or equal Example 2 y = x 2 − 2 The only difference with the first graph that I drew (y = x 2) and this one (y = x 2 − 2) is the "minus 2" The "minus 2" means that all the yvalues for the graph need to be moved down by 2 units So we just take our first curve and move it down 2 units Our new curve's vertex is at −2 on the yaxisExample The point P(4,2) lies on the curve y = √ x a) If Q is the point (x, 2(1x) x−1 = 1 2 x−1 1x 1 x−1 = 1 I've included a plot of the function y = √ x and the tangent line y = x/4 1 below as a check to make sure I have the right answer Everything looks good!
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The axis command reveals that the plot command believes that all yvalues equal zero for values of x between − 1 and 1 Note the horizontal line connecting the right and lefthand halves of the hyperbola in Figure 42 This line simply does not belong in this image, as xvalues between − 1 and 1 are not in the domain of of y = √ x 2 − 1 y = x 2 ⇒ x 2 = y x 2 = y parabola is not defined for positive values of y hence parabola will be below Xaxis opening downwards and passing through (0, 0) x y 2 = 0 is a straight line To find point of intersection of parabola and straight line solve the parabola equation and the straight line equation simultaneouslyPlot (2,45) and (3,7) Example 2 Estimate the coordinates of P and Q given below Using the Pythagorean formula from plane geometry we can arrive at a formula for the distance between two points in terms of the coordinate of those points Let P (X 1,Y 1) and Q (X 2,Y 2) be given Denote the distance between P and Q by d (P,Q) See Figure 3
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Find the coordinates of the centroid of this body (Hint Two coordinates can be found by symmetry, and an integral is needed only for one of them) (d) Now assume that the density of this solid is δ(x, y, z) = y √ x 2 z 2 What is its mass?Explore nonlinear graphs 1 Here is a table of values for y = x2 x –4 –3 –2 –1 0 1 2 3 4 y 16 0 9 a) Complete the table of values b) Explain why y isLearn college algebra 1 with free interactive flashcards Choose from 500 different sets of college algebra 1 flashcards on Quizlet
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(a) y = x2 (b) y =lnx (c) y = x2 sin(x)(d) y = sin(x) x 23 Acceso directo a las pantallas de Plot functions Cuando te encuentres en la pantalla de entrada de ecuaciones (Equation Entry), puedes acceder al formulario Plot Window pulsando HF2 Análogamente, si estás en Plot Window, puedes acceder a Equation Entry, pulsando HF1(b) u(x,y) = ln(x2 y2)3/2;% same as x=0 02 04 06 08, >> x= a∆xb;
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2 Identify in this plot the graphs of (13 x) 2, (1 2 x) 2, x2, (2x)2, and (3x)2Notice that we only need to be familiar with the one basic function x2 in order to "understand" the other functions (cx)2 Theorem 2 Replacing x by cx in a function y = f(x) results in a horizontal stretching or compressionArsinh x ≡ lnx √(x 2 1) 2 Plot Archyperbolic sine is antisymmetric function defined everywhere on real axis Its plot is depicted below — fig 1 Fig 1 Plot of the archyperbolic sine function y = arsinhx Function codomain is entire real axis 3 Identities Property of antisymmetry arsinh− x = −arsinh x ReciprocalMath 16A Midterm 1 (Practice 3), Page 2 of 5 2 (25 points) A bank has a saving account in why interest is compounded continuously If the amount in the account doubles every 30 years determine what the annual interest
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Find the area of region bounded by the curves y=sin(pi/2*x)and y=x^22x calculus what is the area of the region bounded by the curves y=x^2 , y=8x^2 , 4xy12=0 calculus review please help!Section 101 Graphing Square Root Functions 545 Comparing Graphs of Square Root Functions Graph g(x) = − √ x − 2 Compare the graph to the graph of f (x) = √ x SOLUTION Step 1 Use the domain of g, x ≥ 2, to make a table of values x 23 4 5 6 g(x) 0 −1 14 17 2 Step 2 Plot the ordered pairs Step 3 Draw a smooth curve through the points, starting at (2, 0)(c) u(x,y) = sinxcoshycosxsinhy Solution (a) If u(x,y) = x2y2, then u xxu yy = 22 = 4 6= 0 Therefore u(x,y) = x2y2 is not a solution (b) If u(x,y) = ln(x2 y2)3/2 = 3 2 ln(x2 y2), then we get u x = 3x x2 y2, u y = 3y x2 y2, u xx = 3 −x2 y2 (x2y2)2, u yy = 3 x2 −y2 (x2 y2)2
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Consider the following y=√(x2)²(x772 y=0 X = 2 X = 7 (a) Use a graphing utility to graph the plane region bounded by the graphs of the equations 1 2 7 2 1 0 2 Maple Generated Plot C 5 3 T77 77 2 (a) Use a graphing utility to graph the plane region bounded by the graphs of the equations (b) Use the integration capabilities of the graphing utility to approximate the volumeAnswer x= 2√2 and x = √2 Solution Given, x² √2x 4 = 0(1) Equation (1) is aEzplot (y) grid on hold y = (x1)^2 1;
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View hw5_solpdf from MATH 214 at Universiti Teknologi Mara Math 214 — Solutions to Assignment #5 111 10 Let x = t2 , y = t3 (a) Sketch the curve by using the parametric equations to plot(e) Compute the center of mass of the solid if the density is δ(x, y, z) = y √ x 2 z 2Z2 1 −x2 4x 1− (−x3 7x2 −10x 3)dx = Z2 1 x3 − 8x2 14x−2dx This is of course the same integral as before, because the region between the curves is identical to the former region—it has just been moved down by 2 x y x and y = x2 ⇒ 8 y = √ x and y =
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$\begingroup$ Draw the graph of $2xy=x^2y^2$ in cartesian coordinates and the graph of $\phi = \frac{\pi}{8} \frac{\pi n}{2}$ in polar coordinates Lo and behold, they are the same $\endgroup$ – Bernard Masse Jul 3 '18 at 1316Y=x^2 and y=2x intersect at (2,4) and (1,1) By inspection of a plot on Desmos the area between these lines will be between 4 and 5 square units Area = S from 2 to 1 of x^2 (2x)dx = S from 2 to 1 of (x^22x)dx = x^3/3 from 2 to 13 O plot3d({sqrt(9x^2), sqrt(9y^2)},x=33,y=33);
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X Y x=y2 y=x2 (1,1) (4,2) Figure 2 The area between x = y2 and y = x − 2 split into two subregions If we slice the region between the two curves this way, we need to consider two different regions Where x > 1, the region's lower bound is the straight line The equation of the upper half of the sideways parabola is y = √ x and thatView Notes M25B__ans from MATH M25 at Moorpark College MATH M25B Exam III Name 1 (5 pts) Find the surface area of revolution obtained by rotating the curve y = 25 x2 about the xaxis, for x(a) y = √ x, (b) y = √ x−1, (c) y = 1 x2 1, (d) y = 1 x En cada caso borra la ecuación anterior con DEL y añade la nueva ecuación con ADD Observa que cada vez se crea una nueva función Cuando acabes las representaciones, accede al menú de variables y observa las funciones Y1,Y2,Y3, que ha creado el sistema
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(d) Find the xcoordinates of each point where the slope of the tangent line is zero (e) Plot y2 = x3 x2 − 6x on your calculator (Hint Plot y = √ x3 x2 −6x and y = − √ x3 x2 −6x on the same set of axes) Confirm your answers to parts (b),(c) and (d) (4) The Bessel function of order zero, y = JWe have three unknown quantities here x1, y1 (the coordinated of the tangent point) and k Let us find three equations for that An equation of the tangent to this ellipse passing through point (x1,y1) is (x1*x)/4(y1*y)/9=1 or 9x1*x4y1*y=36 4y1*Ezplot (y) axis (5 5 0 5) 6 Activity (Editor) 1 Practice Activity #2 x = 04pi y = cos x cos 2x y = e x y = sin x sin 3x y = √ x 2 8 x = 0014*pi;
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See below (Delta y) /(Delta x)=( f(xDelta x)f(x))/(Delta x) and (dy)/(dx) = lim_(Delta x>0)(f(xDelta x)f(x))/(Delta x) so dx cannot be equal to 1 Applying it to% What happens if you skip the semicolon?X meters from the top of the tank The w eigh t of sheet (densit y times v olume) is (103)(98)(2)(1)(dx) N The distance this sheet tra v els b efore lea ving the tank is x meters The total w ork required to pump half the ater out is 11/2 0 (196)(103)xdx = (98)(103)x2 /2 0 = 245×103J 9 E Slice in to crosssections p erp endicular the y
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Instructor Barry McQuarrie UpdatedFor three variables, a level set is typically a surface, called a level surface EXAMPLE 1415 Suppose the temperature at (x,y,z) is T(x,y,z) = e−(x2y2z2) This function has a maximum value of 1 at the origin, and tends to 0 in all directionsOf y = √ x The rule y = √ −x for x ≤ 0 yields a graph which is the reflection of the graph of y = √ x in the yaxis All graphs of the form y = a −(x −h) k will have the same basic shape as the graph of y = √ −x Example 4 Sketch the graph of y =−2 √ x −1 3 Solution The graph is formed by dilating the graph of y
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Graph the parent function of g(x) = 1/4 ∙ √x On the same graph, plot g(x) using vertical compressions Solution We've already learned that the parent function of square root functions is y = √x Let's go ahead and graph y = √x firstLet f be the function defined by f(x)=xe^(1x) for all real numbers x a Find each interval on which f is increasing b Find the xcoordinate of each point of inflection of the graph of f Calculus The curve y = 11x 24 x^2 cuts the xaxis at points A and B, and PN is the greatest positive value of the y coordinateSolution for Find the area of the surface given by z = f (x, y) that lies above the region R f(x, y) = √(a2 − x2 − y2) R = {(x, y) x2 y2 ≤ a2}
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Section 102 Graphing Cube Root Functions 553 Comparing Graphs of Cube Root Functions Graph g(x) = − √3 x 2 Compare the graph to the graph of f (x) = √3 —x SOLUTION Step 1 Make a table of values x −10 −3 −2 −16 g(x) 210−1 −2 Step 2 Plot the ordered pairs Step 3 Draw a smooth curve through the points The graph of g is a translation 2 units left and a refl ection in the1 Creating Vectors and Matrices Row vectors there are many ways of creating a vector Explicit list >> x=0 1 2 3 4 5;
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