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WayneDeguMan Vertical asymptotes occur when the doniminator is zero ie when \displaystyle{2}{x}^{{2}}{3}{x}{2}={0} or, (2x 1)(x 2) = 0 HenceCancel the common factor Divide ( x − 3) ( x 1) ( x 3) ( x 1) by 1 1 Divide 0 0 by 2 2 If any individual factor on the left side of the equation is equal to 0 0, the entire expression will be equal to 0 0 Set the first factor equal to 0 0 and solve

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Graph y = 2x 1Graphing a line requires two points of the line which can be obtained by finding the yintercept and slope 3 Answers Douglas K Given x2 3xy y2 = 0 Differentiate each term with respect to x d(x2) dx 3d(xy) dx d(y2) dx = d(0) dx Use the power rule, dy dx = nxx−1, on the first term 2x 3d(xy) dx d(y2) dx = d(0) dx Use the product rule, d(xy) dx = dx dx y x dy dx = y x dy dx on the second termExtended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music

 Ex , 3 Find the area of the region bounded by the curves 𝑦=𝑥22, 𝑦=𝑥, 𝑥=0 and 𝑥=3 Here, 𝑦=𝑥22 𝑦−2=𝑥^2 𝑥^2=(𝑦−2) So, it is a parabola And, 𝑥=𝑦 is a line x = 3 is a line x = 0 is the yaxis Finding point of intersection B & C Point B Point B is intersection Explanation Sort the x terms and y terms x2 −x y2 2y = −1 Now, complete the square for each variable x2 −x 1 4 y2 2y 1 = −1 1 4 1 Don't forget to balance both sides of the equation (If you add something to one side, add it to the other side as well) (x − 1 2)2 (y 1)2 = 1 4 This is in the standard form of a circle1) is a critical point The second derivative test f xx = 2;f yy = 2;f xy = 0 shows this a local minimum with

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The rst equation is an exponential growth equation with solution x= ae4s, and the second is readily integrated to yield y = s This means the third becomesdz ds = 2s so that z = s2 log(8 a2) To invert the (x;y) (a;s) system, simply note that a= xe4s= xey Thus z= u(x;y) = s2 log(8 a2) = ySelect a few x x values, and plug them into the equation to find the corresponding y y values The x x values should be selected around the vertex Tap for more steps Replace the variable x x with − 2 2 in the expression f ( − 2) = − ( − 2) 2 − 2 ⋅ − 2 − 1 f ( 2) = ( 2) 2 2 ⋅ 2

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