(. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

Q: i) dt (1+t)3 j) S(sin?x cos x)dx x+3 k) S: -dx x2+6x-11

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Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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Q: Find the differential and evaluate for the given x and d/x of the function, y = tan x, x = 0, dx =…

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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 differential of the given functions. a) f(x) = sin(cos(22)) CoS %3D 2x b) g(x) x3 – 7x

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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: dx/dt + 4x = cos(2t), x(0) = -1 Find x(t)

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Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

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Q: 3. Find the linear approximation to g(z) = cos(z + 1) at z = 0. Use the linear approximation to…

A: The formula to find the linear approximation L(z) of a function fz at point z=z0 is: Lz=fz0+f'z0z-z0…

Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

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Q: 27. w = xy + yz+ zx, x = r cos 0, y = r sin 0, % = r0; %3D dw dw when r = 2,0 = T/2 Ər' d0

A: Given that,  w=xy+yz+zx , x=rcosθ, y=rsinθ and z=rθ. To determine the value of ∂w∂r, when, r=2 and…

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: 1. Find the differential of w = x cos y – y sin x.

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Q: Find a homogeneous (linear) DE with a following FSS: y1(x) := 1; y2(x) := sin(5x); y3(x) := cos(5x)

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Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: b) f(x) = In(1 – 3x) %3D c) f(x) = cos(t³) dt

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

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Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: 4.) (w° + wx²- x ) dw t ( x° t w? x - w) dx = 0 ( 2x +y cos xy) dx t x cos xydy COS X

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Q: Find F′(x).

A: Given- Fx=∫02xcost4 dt To find- F'x Concept Used- The Leibnitz's theorem as  ddx∫gxhxft…

Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: f(x) = | e 'cos(af(s))ds, 0<x< 1, 0 < a < 1, -SX

A: Given: f(x)=∫01e-sxcosαf(s)ds, 0≤x≤1, 0&lt;α&lt;1

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: z=ye^(xy) - e^(xy) sin x +xy, find əzləx * O y^2 e^(xy)-e^(xy) cosx-y sinx e^(xy)+y y^2 e^(xy)-y…

A: Given z=yexy-exysinx+xy

Q: f(x) = In(2 + cos x). -2.125, xk+1 = Ik +0.5, yk = f (xk), k E N To = %3D %3D = 0r

A: The function is fx=ln2+cosx Conditions: x0=-2.125, xk+1=xk+0.5, yk=fxk, k∈ℕ xk+1=xk+0.5…

Q: (a) Find the differential dy. y = tan(x) dy = sec?(x) (b) Evaluate dy for the given values of x and…

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Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

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Q: h(x) = x² In(x) s(y) = In(cos(y) +2) a. с. %3D b. p(t) = In(t) et +1 d. z(x) = tan(In(x)) е. m(z) =…

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 2. F(x) = fr Cos t dt %3D

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Q: l. sin (x) dA where D is bounded by y cos x, 0 <x < /2, y = 0, and x = 0.

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Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

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: At what points (x, y) in the plane are the functions in Exercises 31–34 continuous?

A: Since you have asked multiple question, we will solve the first two question for you. If you want…

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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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: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: 5 The function f(x, y) = | x' cos is homogenous inx and y of degree

A: Given that: f(x, y)=x2cos2yx-y2+x3y

Q: F(x) = [,**dt COS x 1 %3D 19

A: Answer is given below

Q: 4] I Let w = 5 cos(xy) – sin(xz); x = 1/t, y = t, z = dw using an appropriate form of the chain…

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Q: 3. Find the derivatives of y with respect to x: a) y = xe* – e* b)' y = e(4x+±) c) y = e (sin x +…

A: To find- Find the derivatives of y with respect to x: y = xex - ex y = e4x + 1x y = exsinx + cosx y…

Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

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Q: implicitly dx

A: Solved below

Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)