Given, f (x, y, z) = sin (x²y – z)+ cos (x? – yz). Find fz. cos (x²y – 2) – sin (x² – yz) - cos (x²y – 2) – sin (x² – yz) sin (x²y – z) + cos (x – yz) cos (x²y – 2) + y sin (x² – yz)

Q: Evaluate |F. di where F = ( – 4z, F(t) = (t, sin(t), cos(t)), 0 < t < T %3D

A: Introduction: the curve C ⊂U is defined as follows for a scalar field with functionf: U Rn→ R, a…

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Q: Let x (t) =y(t) +sin(t), x2(t)=y (t) then x2(t)= x,(t)- cos(t) Select one: O True False

A: given x1(t)=y(t)+sin(t) , x2(t)=y'(t)

Q: Find a harmonic conjugate of the function u(x, y) = arctan(x/y)− 6

A: Solution :-

Q: (a) fr = 4xz2, fy = yz and f; = xz 2 sin (x), fy = cos(x)y and f: = e" z z + y? If, f = = frâ + fyŷ…

A: a) Given f=fx+fy+fz and F→=fx x^+fy y^+fz z^ and  fx=4xz2, fy=yz, fz=xz So, we have f=fx+fy+fz…

Q: 2x3y3 + cos(x. y) lim (x.y)-(0,0) (x + 1) 2 sin T +y

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Q: dz Given that xy + z³ + sin(xyz), find dx O -2xy – xz cos(xyz) 3z2 + xy cos(xyz) O y + yz cos(xyz)…

A: Detailed solution I have given you...hope you will get it easily...thanks

Q: If z = sin(xy), then dz is A y cos(xy)dx + x cos(xy) dy y cos(xy) + x cos(xy) dy C y cos(xy)dy + x…

A: z= sin(xy)

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Q: 4.10. Suppose P is an integral d-polytope. Show that the dilate (d + 1)P contains an interior…

A: Let's assume that the lattice points in d-Polytope : P=p1,p2,p3,....pn The following figure shows…

Q: 11. Determine the conjugate harmonic function v of u = re² cos(y) – ye² sin(y) such that f(z) = u+…

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Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: 7. Let f(x, y) = 2, where x = 2 cos u and y = 3 sin v. Find fu(x, y) and f(x, y) and y exprees them…

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Q: Let z be a function of x and y defined implicitly from the equation 9ye" - 5 cos(y+ z – 1) = 7x –…

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Q: (b) | F. dĩ, where F(x, y) = (y cos(xy) – 2a, x cos(xy) + 1). 6 Y C 4 3 2 1 2 3

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Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

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Q: Q2:- Find fo, fe , fo if f(p, 0,¤) = p² cos ¢ sin 0. cos O sin 0

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Q: 2. Find (F(r(t))) when F and r are the functions given below. (a) F(x, y) = sin(x) + cos(y) and r(t)…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: dy . If sin (x + y) = xy, what is the expression for xY, dx cos(x + y) – Y - 1- x cos(x + y) – Y - В…

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