The domain of the function y=Vx+1 x> - 1 B x< -1 c) x21 D A)

Q: 9. Use f(x, y) = Vx? + y? to give a linear approximation of v/3.12 + 3.992.

A: Linear approximation to the function

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: f(x, y, z) = x – Vy² + z

A: Take the partial derivative ony by one with respect to x, y &amp; z considering other as constant at…

Q: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

A:

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

A:

Q: f Vf(x, y) = 0, then Duf(x, y) = 0 for all u. %3D %3D

A: True

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

A:

Q: Which of the following represents the distance between (X. (X2. Y2) O A. d = 2 / (x2 +1) + (y2 +Y1)…

A: Given two points, A(x1,y1) B(x2,y2) distance d=?

Q: Utt = Uxx, x>0, t > 0, u(x,0) = f(x), u₁(x,0) = 0, u₂(0,t) = 0, where f(x) = { b) Sketch the…

A: solutions are given below:

Q: Let f be a differentiable function of one variable, and let f(p), where p = (x² + y² + z²)'/2. Show…

A:

Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

A:

Q: 15. f(x, y) = xy /x² + y V9 – x² – y? 16. f(x, y) ▪ x + 2y + y? x² – y? 17. f(x, y) *

A: 1.  fx,y=xyx2+y2.  fx,y=9-x2-y2x+2y3.  fx,y=x2+y2x2-y2

Q: af Given f(x, y) = In(6x² + 8y²) then %3D

A:

Q: a) What is the dimension of {(x, y) E R² : x + y = 0}?

A:

Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

A:

Q: Let f(x,y) = ax + by2 af where a and b are constants. If of at x = 1 and %3D ху y 2, then the…

A: Introduction :

Q: Given f(x, y) = et" Y° – a°y°, show that fæy = fyx· 93 fyæ- %3D

A:

Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

A:

Q: Suppose that f(x, y) = y/x³ + 1 at which {(x, y) | 0 < y < x < 1}. %3D D

A:

Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

A:

Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

A:

Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x&gt;0,     t&gt;0ux, 0=fxu0, t=0

Q: Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy −…

A: Given

Q: If f(x, y, z) = xy + z?x - 3yx z?, find fxy ?

A: If fx,y,z=xy+z2x-3yx2z2 Find fxy ?

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: The range of f(x,y) = 2 - x2 + 4y² is : O [0,2] O xy-plane Joo+7] O

A:

Q: x2 B) If w = x".f then show that: %3D x. Wx + y. Wy = nw.

A:

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

A:

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

A:

Q: The domain of f(x,y) = In ry is points (x, y) in the first quadrant. Select one: O True O False

A:

Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

A:

Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

A:

Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: %3D 23. f(x, y, z) = 2x + z? subject to x² + y? + 2z? = 25

A: Lagrange's Multipliers: The Lagrange method is used to maximize or minimize a general function…

Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

A:

Q: x² + 5x ,14.f(c) = = 14 f(x) on interval %3D %3D x - 1

A:

Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

Q: f(x, y) = e&z– 4y af af ду

A:

Q: Given f(x, y) = x® + 3xy4 – 2y°, find f-(x, y) = fy(x, y) =

A: If f(x, y) is a function then, fx(x, y)  is differentiation of f with respect to x making y variable…

Q: If u(x.y) and v(x.y) are differentiable, than, is it necessary that f(z)=u(xy)+iv(x.y) is also…

A: We know complex numbers are of the form ,  z = x + i y. Here , x = Real part of complex number  and…

Q: The domain of f(r,y) = In xy is points (z, y) in the first quadrant. Select one: O True O False

A: I have given an answer in step 2.

Q: 16. f(x, y, 2) = y - Vr? + z?; P(-3, 1, 4); a 2i-2j-k

A: To find the directional derivative of f at P in teh direction of a So, given f(x,y,z)=y-√(x²+z²);…

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.