(R, d), where d(r, y) = |r – y|, is separable. %3D

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: The joint PDF of X and Y is given as S2, 0< x< y<1 f(x,y) (0, otherwise

A:

Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

A:

Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

A:

Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: What is the integrating factor of 2y (y - r) dy = dr? %3D O y? 2y

A: Topic = Differential equation

Q: af Find a d () + In (). of the function f(x,y) = arccot and ду

A:

Q: JK = 4x + 8, %3D KL = 5x + 6, and JL = 86, %3D Find KL. J K L

A:

Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

A:

Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

A:

Q: Use the formula f(x) × f(xo) + f' (xo)(x – xo) - to obtain the local linear approximation (y) of 2…

A:

Q: Find the linearization L(x, y) of the function f(x, y) at P0 Then find an upper bound for the…

A: We need to determine the linearization of the function: f(x, y)=xy2+ycosx-1 at P01, 2 over R:…

Q: 2. Find frxz for f(x, y,z)= z² e³xy

A:

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

A:

Q: 1 F (s) = s (s +1) %3D

A: Given: L-11ss+1

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

A:

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: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

A:

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

A:

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

A:

Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: (2t + 4 dt = J t² +1 antidifferentiation c) Evaluate (Don't forget to include the constant of.

A: Find the integration of (2t+4)/(t2 +1)

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the…

A: Given: hx=x4 To approximate the values of 34 and 44 using linear approximation of hx. Note: the…

Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: 3. Find an admissible extremal for the problem of minimizing J[a] {Gi² + xi + x + à} dt with x(0) 1…

A:

Q: A² = x²y 2 + 2y = y + 3 z ³² x ² 2 5 근 SD • A dv = ? (Do > y 2 - 2 d 1 divergence)

A: Given A→=x6yx^+2y5zy^+3z3x4z^

Q: Find fr and fy- f (x, y) = | 5e dt %3| fa(x, y) = fy(x, y) =

A: We apply fundamental theorem of calculas and solve it.

Q: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).

A:

Q: dy + ydx %3D = 3x²y?dx,

A:

Q: given z= f(x,y), where x = g(s,t) and y = h(s,t). chain rule for dz/dt is

A:

Q: dw Use chain rule to find dt if w = xez, x = t², y = 1- t, z = 1+ 2t.

A: Given w=xeyz, x=t2, y=1−t and z=1+2t We have to find dwdt by using chain rule. Hence, by chain rule…

Q: Compute SA f dA for A = {(x, y) E R² ; x > 0, y > 0 and æ + y < 1} and f: A → R, ƒ(x,y) = xy.

A:

Q: dy The D.E. y2 – a? - can be classified as %3D dæ (A) First-order linear (B) Separable (C)…

A: We break this into simplier form then identify it's property.

Q: F(r, y) = is a homogeneous function of degree 1. True False

A: We have to check degree of homogeneous function.

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation