√99以上 x/2 y/4=6 x/5-y/2=0 281021

Solution By the Chain Rule formulaExpress your answer in simplest radical formSketch the graph of the parametric equations x = cos2t, y = cost 1 for t in 0, π Solution We again start by making a table of values in Figure 1022 (a), then plot the points (x, y) on the Cartesian plane in Figure 1022 (b) The curves in Examples 1021 and 1022 are portions of the same parabola (y 1)2 x = 1

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X/2 y/4=6 x/5-y/2=0-Weekly Subscription $249 USD per week until cancelled Monthly Subscription $799 USD per month until cancelled Annual Subscription $3499 USD per year until cancelledAll its eigenvalues are nonnegative (a) Show that λ = 0 is an eigenvalue with associated eigenfunction y0(x) = x (b) Show that the remaining eigenfunctions are given by yn(x) = sinβnx, where βn is the nth positive root of the equation tanz = z Draw a sketch showing these roots

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Learning Objectives 521 Recognize when a function of two variables is integrable over a general region;Z = 1 2t (02) L 2Y=x^21 (Graph Example), 4x2=2 (x6) (Solve Example) Algebra Calculator is a calculator that gives stepbystep help on algebra problems See More Examples » x3=5 1/3 1/4 y=x^21 Disclaimer This calculator is not perfect Please use at your own risk, and please alert us if something isn't working Thank you

 Transcript Ex63, 4 Solve the following system of inequalities graphically x y ≥ 4, 2x – y < 0 First we solve x y ≥ 4 Lets first draw graph of x y = 3 Drawing graph Checking for (0,0) Putting x = 0, y = 0 x y ≥ 4 0 0 ≥ 4 0 ≥ 5 which is false Hence origin does not lie in plane x y ≥ 4 So, we shade the right side of line Now we solve 2x – y < 0 Lets first draw graphX→0 x4e x2 5x4 = lim e 2 5 = 1 5 6= 0 The limit does not exist because there are two different approaches that give different limiting values (d) lim (x,y)→(0,0) x2 sin2 y x2 2y2 We probe the limit by the straightline approaches y = mx which gives lim (x,y)→(0,0) x 2sin y x2 2y 2 = lim x→0 x 2sin2 mx x 2m2x2 = lim x→0Z = 4 9t De nition 01 Two lines L 1 and L 2 with direction vectors v 1 and v 2, respectively, are i) perpendicular if v 1 v 2 = 0, and ii) parallel if v 2 = kv 1 for some nonzero scalar k Example 04Perpendicular lines Determine whether the lines (01) L 1 x = 6 t;

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Question What is the value of y in the formula shown when x = 4/5 ?3y/4 0 f(x,y)dx Z 5 4 dy Z√ 25−y2 0 f(x,y)dx b) Se trata de la regi´on comprendida entre la par´abola y = x2/4−1 y la recta y = 2−x6 2 2 8 Al invertir el orden de integraci´on, la integral se descompone as´ı I = Z 0 −1 dy Z 2Example A circle with center at (3,4) and a radius of 6 Start with (x−a) 2 (y−b) 2 = r 2 Put in (a,b) and r (x−3) 2 (y−4) 2 = 6 2 We can then use our algebra skills to simplify and rearrange that equation, depending on what we need it for

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The function f X Y ( x, y) is called the joint probability density function (PDF) of X and Y In the above definition, the domain of f X Y ( x, y) is the entire R 2 We may define the range of ( X, Y) as R X Y = { ( x, y) f X, Y ( x, y) > 0 } The above double integral (Equation 515) exists for all sets A of practical interestFree system of equations calculator solve system of equations stepbystepWe get x = 5 4t;

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ODEs Find the first four terms of the power series solution to the IVP y"2y'y=x, y(0)=0, y'(0)=1 To check our answer, we find the solution using thIntegrate x/(x1) integrate x sin(x^2) integrate x sqrt(1sqrt(x)) integrate x/(x1)^3 from 0 to infinity;Graph y=4/5x2 Rewrite in slopeintercept form Tap for more steps The slopeintercept form is , where is the slope and is the yintercept Write in form Tap for more steps Reorder terms Remove parentheses Use the slopeintercept form to find the slope and yintercept

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(x µx)5 (x µx)5p(x) 0 1/8 0 225 225/8 1 3/8 3/8 025 075/8 2 3/8 6/8 025 075/8 3 1/8 3/8 225 225/8 Σ xp(x) = 15 So (not surprisingly) if we toss a coin three times, we expect 15 heads And, the variance = 6/8 = 3/4 Expectations Page 2Graph y=2 (x4)^26 y = 2(x 4)2 − 6 y = 2 ( x 4) 2 6 Find the properties of the given parabola Tap for more steps 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 a = 2 a = 2 h = − 4 h = 4 k = − 6 k = 6 Since the value of a a is positive, the parabola opens upAlgebra Solve for x (x4)/ (y2)=5 x − 4 y 2 = 5 x 4 y 2 = 5 Multiply both sides of the equation by y2 y 2 x−4 = 5⋅(y2) x 4 = 5 ⋅ ( y 2) Remove parentheses x−4 = 5⋅(y2) x 4 = 5 ⋅ ( y 2) Simplify 5 ⋅(y2) 5 ⋅ ( y 2) Tap for more steps

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 i need help with this differential equation find the general solution of this equation y"5y'6y=0 b) find the particular solution for the equation in (a) satisfying the condition that y=1 & dy/dx=2 when x=0 c) find the general solution of the differential equation y" corresponding elements are equal 2x − y = 10 3x y = 5 (1) Solving equations Adding (1) & (2) (2x – y) (3x y) = 10 5 2x – y 3x y = 15 2x 3x – y y = 15 5x 0 = 15 x = 15/5 x = 3 Putting value of x in (1) 2x – y = 10 2(3) – y = 10 6 – y = 10 –y = 10 – 6 –y = 4 y = –4 Hence, x = 3 & y = –4Integrate 1/(cos(x)2) from 0 to 2pi;

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Then z =0 So this point (x;y;0)satis &es the line equation, ie, x¡2 1 = y ¡4 ¡5 = 03 4 We solve this system to obtain x =2 3 4 = 11 4 y =4¡5 µ 3 4 ¶ = 1 4 z =0 Example 43 Given two lines l1 x =1t;Subtract x from both sides Divide both sides by 2 Divide both sides by − 2 Dividing by 2 undoes the multiplication by 2 Dividing by − 2 undoes the multiplication by − 2 Divide 4x by 2 Divide 4 − x by − 2 Add 2y to both sides Add 2 y to both sidesY = 3t;

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 Let us now find the length L of the curve L = ∫ 1 0 √x'(t)2 y'(t)2dt = ∫ 1 0 √62t2 62t4dt by pulling 6t out of the squareroot, = ∫ 1 0 6t√1 t2dt by rewriting a bit further, = 3∫ 1 0 2t(1 t2)1 2dt by General Power Rule,Y = 2 7t;Select 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 1 1 in the expression f ( 1) = ( 1) 2 − 5 ⋅ 1 6 f ( 1) = ( 1) 2 5 ⋅ 1 6 Simplify the result

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F (x,y) = 2 xy − 2x − 1 4 y2 in the closed triangular region with vertices given by (0,0), (1,0), and (0,2) Solution I The horizontal side of the triangle, y = 0, x ∈ (0,1) Since g(x) = f (x,0) = 2 − 2x, ⇒ g0(x) = −2 6= 0 there are no candidates in this part of the boundary I The vertical side of the triangle is x = 0, y ∈It looks much like aP 318 (3/23/08) Section 144, Chain Rules with two variables Example 3 What are the x and yderivatives of z = F(g(x,y)) at x = 5,y = 6 if g(5,6) = 10,F0(10) = −7,gx(5,6) = 3, and gy(5,6) = 11?

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Y(0) = 0 y(1) = y′(1) (not a typo);Y'' y = 0, y(0)=2, y'(0)=1 Natural Language;Steps for Solving Linear Equation x = 2 y 5 x = 2 y − 5 Swap sides so that all variable terms are on the left hand side Swap sides so that all variable terms are on the left hand side 2y5=x 2 y − 5 = x Add 5 to both sides Add 5 to both sides

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 Let A be the area bounded by y=x,y=2x, and y=0 => A=int_0^1int_y^(2y)dxdy=1 First, a good thing to do would be sketch the graph So, we are looking for the area of that triangle Take note of the points of intersection Here we are dealing with y=2x and y=x So we set both equations equal and get x=2x add x to both sides 2x=2 divide both sides by 2 x=1 So,View more examples » Access instant learning tools Get immediate feedback and guidance with stepbystep solutions and Wolfram Problem Generator LearnX^2 2 y^2 = 1 Natural Language;

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Example 5 X and Y are jointly continuous with joint pdf f(x,y) = (e−(xy) if 0 ≤ x, 0 ≤ y 0, otherwise Let Z = X/Y Find the pdf of Z The first thing we do is draw a picture of the support set (which in this case is the first522 Evaluate a double integral by computing an iterated integral over a region bounded by two vertical lines and two functions of x, x, or two horizontal lines and two functions of y y;Piece of cake Unlock StepbyStep Natural Language Math Input

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 Facebook Whatsapp Transcript Example 17 Solve the pair of equations 2/𝑥 3/𝑦=13 5/𝑥−4/𝑦=−2 2/𝑥 3/𝑦=13 5/𝑥−4/𝑦=−2 So, our equations become 2u 3v = 13 5u – 4v = –2 Hence, our equations are 2u 3v = 13 (3) 5u – 4v = – 2 (4) From (3) 2uThen type x=6 Try it now 2x3=15 @ x=6 Clickable Demo Try entering 2x3=15 @ x=6 into the text box After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x3=15 2(6)3 = 15 The calculator prints "True" to let you know that the answer is4x425x26=0 Four solutions were found x = 1/2 = 0500 x = 1/2 = 0500 x = ± √6 = ± Step by step solution Step 1 Equation at the end of step 1 ((4 • (x4)) 52x2) 6 = 0

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523 Simplify the calculation of an iterated integral by changing the order of integrationProblems 63 Solutions 1 Solve the initial value problem xy0 y = x, y(2) = 5 Solution First solve the homogeneous equation xy0 y = 0, for which the variables separate dy/y = −dx/x This integrates to lny = −lnxC = ln(1/x)C, which in turn exponentiates to4 0 0 6 1 1 8 2 2 3 Figure 1412 f(x,y) = x2 y2 (AP) As in this example, the points (x,y) such that f(x,y) = k usually form a curve, called a level curve of the function A graph of some level curves can give a good idea of the shape of the surface;

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Y 3 2 y − 4 3 = y 6 5 Variable y cannot be equal to any of the values 6,3,4 since division by zero is not defined Multiply both sides of the equation by \left (y4\right)\left (y3\right)\left (y6\right), the least common multiple of y3,y4,y6 Variable y cannot be equal to any of the values − 6, − 3, 4 since division bySOLUTION 1 Begin with x 3 y 3 = 4 Differentiate both sides of the equation, getting D ( x 3 y 3) = D ( 4 ) , D ( x 3) D ( y 3) = D ( 4 ) , (Remember to use the chain rule on D ( y 3) ) 3x 2 3y 2 y' = 0 , so that (Now solve for y' ) 3y 2 y' = 3x 2, and Click HERE to return to the list of problems SOLUTION 2 Begin with (xy) 2 = x y 1 Differentiate both sidesExtended 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

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X^2y^2=1, (x2)^2 (y1)^2=4 WolframAlpha Volume of a cylinder?Graph y5=2(x4) Move all terms not containing to the right side of the equation Tap for more steps Add to both sides of the equation Add and Use the slopeintercept form to find the slope and yintercept Tap for more steps The slopeintercept form is ,(a) there is no m~as needed in De nition 1141 (b) f x(0;0) does not exist and using part (c) of remark 1142 Solution (a) Let m~= hm 1;m 2iIf fis di erentiable at (0;0) then m 1 and m 2 can be chosen so that lim (x;y)!(0;0) f(x;y) f(0;0) m

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Z =4¡t l2 x =2t;Extended 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, musicIf x and y are positive real numbers for which (x y)^2 (x y)^2 = 10 and (x y)^4 (x y)^4 = 98, what is the value of xy?

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Extended 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 #x^2 6x y^2 4y = 12 Then take 1/2 of the 'b' term for both quadratic expressions, square those values and add them to both sides #x^2 6x 9 y^2 4y 4 = 12 9 4 (x 3)^2 (y 2)^2 = 25 Circle centered at (3,2) with radius = 5Integrate x^2 sin y dx dy, x=0 to 1, y=0 to pi;

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X¡2 1 = y ¡4 ¡5 = z 3 4 3 (b) If this line crosses xy ¡plane somewhere at (x;y;z);Answer (1 of 9) \frac{x1}{2}= \frac{y2}{3}= \frac{z1}{4} is line passing through P(1,2,1) and having direction ratios 2,3,4 \frac{x3}{1}= \frac{yk}{2}= \frac{z0}{1} is line passing through Q(3,k,0) and having drection ratios 1,2,1 If the two lines intersect, the line PQ and the two liFree linear equation calculator solve linear equations stepbystep

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