poin If g(u) —D V9u + 3 then g' (u) =

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = 1 + xy2 - 2z2

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Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: 2. -1z"cosdz zl=1

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Q: 2. y"-y-6y = u(t – 1) – u(t – 4); y(0) = 1, y(0) = -1

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Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: - r)rdrde 32(V2-1) 16(VZ-1) c. VZ-1) 4(VE-1), S(V2-1) a. d. 3. 3 3 e. 3.

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Q: Differentiate the function.

A: Consider the following equation: Gy=ln2y+15y2+1 Differentiate the above equation with respect to y:…

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: y show that = 0. . If z: x² + y² II

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Q: Fill in each blank so that the resulting statement is true.

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Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

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Q: (2xy + 3x²)e, + (x² – 2yz + 2y)e,- (e2 +y²)e, olan f(x,y,z)

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Q: 4' for T- T2• T, and T- T1• T2. x - 5y, 4x + 2y) y, 0)

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Q: 2. y" – 2y' – 3y = e²", y(0) = 1, y (0) = 0, Yp(t) = -e2' /3 %3D

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Q: y"-2y'+y = e* Inx

A:

Q: (i) Find the covariance of Y1 and Y2, Cy, Y,

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Q: Find the general solution of y" – y' – 2y = cosh 2t.

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Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

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Q: .3 S(3 – e3*)²dx

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Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: e-X f(x, у) %3D x2 + y2

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Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: V1-x2 3. Evaluate S S /1-x²-y² dxdydz V1-x2-y2-z2

A: We will solve the following.

Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

A:

Q: 5 Use implicit derivation to find y. x² +y +z =e"-

A: Given,           x2+y2+z2=exyz

Q: px + qy=z-a √x² + y² + z²

A:

Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

A:

Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: Lion 1-y If x = Show that 1+y dy V1-y

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Q: 2- V 1F 3 5 -1- -2F a -3-

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Q: Solve f, e-+ n² dt. 6.

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Q: 3. Find the general solution using the method of Variation of Parameters. y" + y = = sect

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Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

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Q: = (y² – z² +3yz – 2x of the following is/a

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Q: Мaximize p = 10x + 10y + 15z subject to + z s 12 X y - 2x 2y + z 2 14 -y + z 2 4 x 2 0, y 2 0, z 2…

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Q: If y = Eo(k + 1)z*+3 then y' = .

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Q: 48xyz < (3x + 2y)(y+ z)(3x + 2z) for every x, y, z E [0, +∞[.

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Q: - 6х + 2у, dt dy -3х + 1у dt

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Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: f Lan 2X e *3 of +sec2X Pinel dy o

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Q: g) Suppose y² + [S(z)]² = 2, then (7,1)

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Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

A:

Q: Find formulas for dy and Ay if y = x² – 7x + 3.

A: To give the formula dy = f'(x) dx and    ∆y = f(x+∆x) -f(x)

Q: y = (2x + 1)v2x+1

A: