Given f(x, y) 70x + 60y – 2? – 3y? – xy - - evaluate f(1, 3). f(1, 3) =

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

A:

Q: IF f(x,y) = y³e-5x find fryy at (0,1)

A: We need to find the partial derivative fxyy of f(x, y) = y3e-5x at (0, 1). Let us first find fxyy.…

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: *z + yz? + 2ry? - = 0 ve z = f (x, y) ise =? what is the f(0,1) at

A:

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Y Is the midpolnt of XZ.If XZ 8x-4 and YZ = 3x +1, find x.

A: Given Y is the mid-point of line segment XZ XZ = 8x-4 YZ = 3x+1   to solve the given question use…

Q: Find dy for given Values OF x and AX y= 4x315x X=-3 and AX = 0.3

A:

Q: 4: Find the approximate value of f(-2.001, 1.002) where f(x, y) 3x?y + y? – xy +1

A:

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

A:

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

A:

Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

A:

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

Q: Se-2t if 0 3,

A:

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

A:

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

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

A:

Q: .Determine if F(x, y) = (2xy + y-2)i + (x² – 2xy-3)j for y > 0 is conservative.

A:

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

A:

Q: 2 The Range (Ry) of y = v9 – x² -

A:

Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

A:

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find fr, fu, and f.. -0.5 f(x, y, z) = (4x² + 6y² + 3z²) fz = fy = f: =

A:

Q: O For the bvp d²y - 9y = 3x, y(0) = y(1) = 0 the Green's functions G(x, §) satisfies d²G(x,£) -…

A: The greens function satisfies the homogeneous differential equation, not the non - homogeneous…

Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

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

A:

Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

A:

Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

A:

Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

A:

Q: The antiderivative of the function f(x) +10z is -5 - 5.0z2+c -10 +2.5z2 + c +5.0z2 +c -5 + 5.0r +c…

A: To find:∫5x2+10x dx

Q: or f(x, y) a + y? – xy +1 -

A: Consider the given function as fx,y=13x3+12y2-xy+1

Q: Q3: 1f f (x,y) = 6x*y5 + 4x*y4 Prove that: f (x,y) * fxxyy fxx * fyy = 1

A:

Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

A:

Q: Find fxxy given that f(x, y) = e^xy^2

A: Given,   f(x,y)=e^x *y^2             we have to find fxxy

Q: If f (x, y) = Vr3 + y3 In (x² + y³)esin(zy+y') + x°y+ 10 , then f. (1,0) O 4

A: Properties of derivative  ddxex=ex ddxxn=nxn-1 ddxsinx=cosx ddx(lnx)=1x

Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y)=3-2x2-2xy-2y2-16x as follows.…

Q: = 0 for F = yz²î +xyj + yzk

A:

Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

A:

Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

A:

Q: 0If z-x"f), show that xZ+JZy=mZ.

A:

Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative

Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

A: