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Over the region D = {(x,y) x2 y2 8} As before, we will find the critical points of f over DThen,we'llrestrictf to the boundary of D and find all extreme values It is in this second step that we will use Lagrange multipliers The region D is a circle of radius 2 p 212 18 81 99 b Two parallel lines are crossed by a transversal What is the value of m?The base is the region enclosed by y = x 2 y = x 2 and y = 9 y = 9 Slices perpendicular to the xaxis are right isosceles triangles The intersection of one of these slices and the base is the leg of the triangle 73 The base is the area between y = x y = x and y = x 2 y = x 2
Ex 63, 23 Prove that the curves 𝑥=𝑦2 & 𝑥𝑦=𝑘 cut at right angles if 8𝑘2 = 1We need to show that the curves cut at right angles Two Curve intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other First we Calculate the point of inters In this section we will start evaluating double integrals over general regions, ie regions that aren't rectangles We will illustrate how a double integral of a function can be interpreted as the net volume of the solid between the surface given by the function and the xy(b) Find the rate of change of V at (1,1) in the direction h3,−4i Solution (a) We have ∇V(x,y) = hV x(x,y),V y(x,y)i = h(x2 −xyy2) x,(x2 −xyy2) yi = h2x−y,−x2yi Since
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If the curves ay x^2 = 7 and y = x^3 cut each other orthogonally at a point, find a asked in Limit, continuity and differentiability by SumanMandal ( 546k points) the tangent and normalTo y= x2 4, whereas for washers the inner and outer sides would both be determined by y= 4 x2 on the top half of the solid and by y= x 2 4 on the bottom half of the solid Since we're using cylindrical shells and the region runs from x= 2 to x= 2, the volume of the solidFactor x^2y^2 x2 − y2 x 2 y 2 Since both terms are perfect squares, factor using the difference of squares formula, a2 −b2 = (ab)(a−b) a 2 b 2 = ( a b) ( a
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Use the Washer Method to set up an integral that gives the volume of the solid of revolution when R is revolved about the following line x = 4 When we use the Washer Method, the slices are perpendicularparallel to the axis of rotation This means that the slices are horizontal and we must integrate with respect to yAbout x = 1Find the volume of the solid obtained by rotating theregion bounded by the given curves about the specified line Sketchthe reVolume V of the solid generated by revolving the area cut off by latus rectum (x = a) of the parabola y^2 = 4ax, about its axis, which is x axis, is given by the formula;
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For graph Y = x^2 Kx 2 to cut x axis y coordinate must be zero thus, x^2 Kx 2 = 0 Now for this equation for solution to be finitly 2 , b^2 4ac > 0 here b = K , a = 1 and c = 2 for every value of K , b^2 4ac will be greater than zero for example k = 0 => (0)^2 4(1)(2) = 8 for k = 1 => (1)^2 4(1)(2) = 9 How do you calculate the arc length of the curve #y=x^2# from #x=0# to #x=4#?V= (π)∫y^2dx, within limit x = 0 to a = (π)∫(4ax)dx, limits 0 to a = 4
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The region bounded by the y = x ^ 2 parabola from the bottom and the y = 4 line from the top is cut by the line y = c and divided into two equal areas A) Draw the region and add a line y = c that seems appropriate Where do they intersect with the parabola, in terms of c?Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyClick here👆to get an answer to your question ️ The straight line y = x 2 rotates about a point where it cuts the x axis and becomes perpendicular to the straight line ax
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The two curves x = y 2, x y = a 3 cut orthogonally at a point, then a 2 is equal to View Answer Write the angle made by the tangent to the curve x = e t cos t , y = e t sin t at t = 4 π with the x axisIf the Curve Ay X2 = 7 and X3 = Y Cut Orthogonally at (1, 1), Then a is Equal to (A) 1 (B) −6 6 (D) 0 Mathematics Advertisement Remove all ads Advertisement Remove all adsFor positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side a b can be cut into a square of side a, a square of side b, and two rectangles with sides a and bWith n = 3, the theorem states that a cube of side a b can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyY = x^2, x = y ^2;F (x,y) is the height of the graph along the z axis The first line is z=f (x,y)=x0², or, z=x, which is a line that rises up above the xy plane at a 45 degree angle and is positioned directly over the x axis (since the x axis is where y=0) When x=0, z=0, when x=1, z=1, when x=2, z=2 That means there is a curtain along the x axis whose
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Find the slope of the tangent to a parabola y = x 2 at a point on the curve where x = ½ A 0 93 Find the acute angle that the curve y = 1 – 3x 2 cut the xaxisHi Mike, y = x 2 2 is a quadratic equation of the form y = ax 2 bx c, let a = 1, b = 0 and c = 2 You can certainly plot the graph by using values of x from 2 to 2 but I want to show you another way I expect that you know the graph of y = x 2 If you compare the functions y = x 2 and y = x 2 2, call them (1) and (2), the difference is that in (2) for each value of x theCalculus Applications of Definite Integrals Determining the Length of a Curve 1 Answer Eric S Use the arc length formula Explanation #y=x^2# #y'=2x# Arc length is given by #L=int_0^4sqrt(14x^2)dx#
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Surface area and surface integrals (Sect 165) I Review Arc length and line integrals I Review Double integral of a scalar function I The area of a surface in space Review Double integral of a scalar function I The double integral of a function f R ⊂ R2 → R on a region R ⊂ R2, which is the volume under the graph of f and above the z = 0 plane, and is given byV(x,y) = x 2−xy y (a) Find the direction of the greatest decrease in the electrical potential at the point (1,1) What is the magnitude of the greatest decrease?Divide 0 0 by 4 4 Multiply − 1 1 by 0 0 Add − 2 2 and 0 0 Substitute the values of a a, d d, and e e into the vertex form a ( x d) 2 e a ( x d) 2 e Set y y equal to the new right side Use the vertex form, y = a ( x − h) 2 k y = a ( x h) 2 k, to determine the values of a a, h h, and k k
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