Find f, and f, and evaluate each at the given point. y' f(x, y) = e*y2, (In 4, 2) f,(x, y) = %3! f,(x, y) = %3D f,(In 4, 2) = fy(In 4, 2) = %3D %3D

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: 3.2= e'-ry ; I=t3 and y = t° %3D

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Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and 0,

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Q: (a) If w = e"yz, where x = and compute dw/dt when t = 0. (b) If f(x, y, z) function of s and t and…

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: Find the linearization of the function f (x) = x at a = 1. a Va lal sin (a) L (1) Using this…

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Q: Let f(r, y, z) = In(r2 + 2) + y?e* – cos(2yz). Find Szya- Find all the relative extrema and saddle…

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Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: Which of the following functions is homogeneous of degree 2/3. option I: 3 f(x, y) = /x² + y2 option…

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Q: If f(x) = xe , x >0 and (Y = ln(X)), then the PDF of Y is %3D (In(1)² (In(y))e ye

A: Answer: ⊙ ey-12e2y

Q: 2 Let f (x) = x on [0, 1] Calculate x dx and x dx by dissecting O, I] oaual narts and hence show…

A: Given

Q: Find all local extrema of the Dirichlet function, defined on (0, 1) by 0, if x is irrational if r =…

A: A function can infinite number of local maxima's and local minima's but there would always be one…

Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

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Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

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Q: Suppose that u and v are differentiable at x = 2 and that u(2) = 4, v(2) = -9, u'(2) = 5, and v'(2)…

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: Let Use Euler's Method with h=.5 ond (X,Y.) -(1,1) to estimate (a, y )

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Q: If x, y, and z are lengths of the edges of a rectangular box, the common length of the box’s…

A: Given If x, y, and z are lengths of the edges of a rectangular box

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

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Q: Let r = x² + y – z and z³ – xy + yz + y³ = 1. Assume that x and y are independent ar is variables.…

A: Introduction :

Q: By using the multivariable chain rule, compute each of the following derivatives. (b) af/ds and…

A: (b) Given function is fx,y=exy Where, x and y is the function of s and t and defined as x,y=s-t,2st…

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

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Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: Using an appropriate linearization, the local linear approximation of f(x) = T + cos x at is Select…

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Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: 2. Suppose that z = f (x, y) and both x and y are functions of a single variable t such that dy t2 –…

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Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: Assume x and y are functions of t. Evaluate dy / dt for the following. y3 = 2x 4 + 6 ;        dx /…

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Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following. y ln x + xey = 1; dx/dt…

A: Solution: Consider the given function is yln x + xey = 1 and dxdt = 5  We have to find dydt at (x,…

Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: z is a function of x and y implicitly defined by Find and i at (x, y, z) = (0, 2, -1) əz Əx Əy y³…

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Q: if (2,y) # (0,0) Let f(x, y) = aª + yª Show that D1f(0,0) and if (2,y) = (0,0) D2f(0,0) exist but f…

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Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Solve the problem. dw Evaluate dv 2 at (u, v) = (5, 2) for the function w(x, y) = xy - In x; x = e…

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Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

Q: given z= f(x,y), where x = g(s,t) and y = h(s,t). chain rule for dz/dt is

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Q: The joint PDF of X and Y is given by f (x, y) = x+ 0 0 and y E (0, 1), derive E[X | Y = y] in terms…

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Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following .xey = 2 - ln 2 + ln x;…

A: It is given that, therefore the time derivative of the given function is, But it is also given…

Q: Assume x and y are functions of t. Evaluate dy over dt for the following. y = 2x 2 + 6 ; dx over dt…

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