29. Let f(x, y) = x² – xy + y² – y. Find the directions u and the values of Du f(1, –1) for which a. Duf(1, –1) is largest c. Duf(1,–1) = 0 e. Duf(1,–1) = -3 b. Duf(1, –1) is smallest d. Duf(1, –1) = 4

Q: 44. Let r(1) = (r2, 41 – 3). Find T(t) and N(1), and show that the de- composition of a(1) into…

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Q: (b) f(x) = where A; E S™ – (det(Ao + x1A1 + ...+ xn An))/m, on {x | Ao + ¤1A1 ++xnAn > ► 0},

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Q: 10. Suppose that f and g are functions of x and y such that dg dy df af ag and dx dy and suppose…

A: The objective of the question is determine the functions f(x,y) & g(x,y) according to the given…

Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

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Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

A:

Q: 25-let F(xs.2)=x-x22 @ Find VF 6 write the equution of tngent Plame to the at Paint (2,1,1). Find…

A: The given function is,  F(x,y,z)=x2y2-xz2 We have to find,  a) ∇F b) Equation of the tangent plane…

Q: 13. If y (x, t) is a function of x and t, prove that i) L. =py (x, p) – y (x, 0) 2. ii) L =p°y (x,…

A: By Bartleby policy I have to solve first 3 subparts

Q: In Exercises 13–24, draw a dependency diagram and write a Chain Rule formula for each derivative.

A: Since, you have asked multiple questions, we will solve the first three for you. If you want any…

Q: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

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Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

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Q: Q1: If Z = f(x·y) + g. Prove that x² - Zxx + x· Zx = y² · Zyy + y Zy. %3D

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Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: iv) if zy = (x)- then zx + Zy = %3D %3D

A:

Q: Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions…

A: Given: z=x2siny x=2s2+3t2 y=4st To find: Using chain rule, ∂z∂s and ∂z∂t ∂z∂s1,-2 and ∂z∂t1,-2

Q: 2) Use Green's Theorem to compute f F. df where F=(3x +4y) i + 2xyj and C is the triangular path…

A: Use green's theorem

Q: 2) Use Green's Theorem to compute f F df where F=(3x + 4y)i + 2xyj and C is the triangular path from…

A:

Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: The linear transformation Dx:C'a,b→Ca,b maps a function fx to its derivative Dxf. Here, given that…

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: 1. Use the Chain Rule to find u and ou for w = x²y3 where x = dw at s2 +t2 and y = ds

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Q: Suppose z x'y' where x-st and y -t -s. Use the chain rule to determine as and a) -2xy't-4yx's;-…

A: The given multivariable function is: z=x2y2 ,       where x=st     and     y=t2-s2

Q: 5. Let u(r, y) = e" cos (2y), then the function u(z, y) provides the following (a) Uzy = Uyr (b) Uzz…

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Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

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Q: For the function f(x, y, 2) = 102° y³z+ 7æy®z4 + 19xz2 + 8y%z4 + 5a° + 17y7a11 + 4xyz +23 compute…

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Q: 7. Which of the following is the potential function for F = (2ху + 1,х2 + 2yz, y? — 2)? а. Ф(х, у,…

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Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint &amp; z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: Thank you!

A:

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: (a)

Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…

A: Line Integral along the given parametric curve.

Q: |-4 Let y =||-3 and u =||-4 7 Compute the distance d from y to the line through u and the origin. d…

A: Solve for the distance

Q: Use the chain rule. If W=u^3 and U=t-1/t+1, find dw/dt when t=1

A:

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: w=x2+y2+z2,  x=cost,  y=sint,  z=et a).…

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: Let f(z) = 5z2 + 4z.  Find u(x,y) if z = 9.6 + 2.9i .

A: Using , complex function properties

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: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

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Q: (A) Evaluate z dz along from z= 0 to z-4+i along curve of c given by the line from z-0 to z= 2i and…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: Find (if any) the relationship between the empty functions u(x,y) = xcos(t²) – ysin(t²), v(x, y) =…

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find aw/as and ôw/at by using…

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Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

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Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

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Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…

Q: Suppose z = 2xy where x = t^2 + 1 and y = 3 - t. Use the chain rule to determine which of the…

A: In the given question the functions are given as z=2xy , x=t2+1 , y=3-t . The objective is to find…

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

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Q: Q2/ Express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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