af (8,9). Let f(x,y)=x?y*. Find ду

Q: 9. If f(x, y) = x³ + 4xy² + y3 %3D show, that f (ax, ay) = a³f (x,y) %3D

A:

Q: Find fx, fy and f z if f(x, y, z) = e*yz In zx. %3D

A:

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: ху f(x,y,z) =- х+у+z

A:

Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

A:

Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

A:

Q: Show: Cov (X,Y) = E[X(Y – μY)]

A:

Q: prove 0x Øx = Øy for X,Y 0x Øx = {x & X: x # x} § Øy={y&Y: y y}

A:

Q: Suppose that ∇fp =〈2, −4, 4〉. Is f increasing or decreasing at P in the direction v =〈2, 1, 3〉?

A: 1) v=2,1,3 v=22+12+33 = 14 u=vv=1142,1,3

Q: Suppose f(x, y, z) =

A: Given,            f(x, y, z)=1x2+y2+z2 and W is the bottom half of a sphere of radius 6.

Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

A:

Q: (d) u =-,v = xy, = a' ху, 21

A: Consider the given information. (d) Consider the given values. u=12-12x2v=xy The equation of the…

Q: Let F(z, v)-v +y+3z+1-0

A:

Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3)

A: The given function is fx, y=ln1+5x3y2. Obtain the partial derivatives as follows. fxx, y=∂∂x…

Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

A:

Q: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

A:

Q: Let fx (x) = x +b, x ∈ [−2b, 2b]. For which b is fX (x) a pdf?

A: Given,  fx (x) = x +b, x ∈ [−2b, 2b] To find the value of b for which fX (x) is a pdf.

Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

A:

Q: Find ƒxx ( x, y)  and ƒxy( x, y).

A: Given, fx,y=3x+yx-1. The objective is to find fxxx,y and fxyx,y.   fxxx,y is found as follows: First…

Q: 5. Given that f (x, y) = sin y, determine fy(x, y).

A:

Q: Let f(x, y) = (- (3z + y))°. Then

A:

Q: af (x,y) f(x, y)=xe"+* 5 у, Х (а) Сompute y af(x,y) X f(x, y)=xe³"+* ,5 у (b) Compute ду y

A:

Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

A:

Q: af Find if f(x,y) = ysin xy

A:

Q: Find the higher-order deriv f"(x) =6Vx – 4 f(5)(x) =

A:

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

A:

Q: f(x, y, z) = 2 ≤ x ≤ 10,0 ≤ y ≤ 4,0 ≤ z ≤4

A:

Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

A:

Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: Let f(r) = Vt3 +1 dt for r2 3. 3

A:

Q: b) Find if f(x, y) = ysin( xy)

A: Givenf(x,y)=ysin(xy)find ∂w∂t

Q: Vy + z f(x, у, 2) 3 (а) f(1, 5, 4) (b) f(6, 7, –2)

A:

Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

A:

Q: Calculate f,e,5 as if f(x,y, z) = z In Vxy

A: here we have to find the functional value

Q: f (x, y) = {* - kx(x — у),0 <x< 2,-х <у<х elsewhere

A: (i) Consider the property for a joint PDF, ∫-∞∞∫-∞∞fx,ydydx=1 Substitute the values,…

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: If f(x,v) = (y)²x ,Verify fy=fx ху

A: Given:fx,y=y2x Now, the value of fxy will be,fxy=∂2f∂y∂x=∂∂y∂f∂x=∂∂y∂y2x∂x Now, the value of ∂y2x∂x…

Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: Calculate F- dS where F (3ry², re", z*)

A:

Q: O Let f(x, y) = (5æ – y)°. Then -

A: We can find the required partial derivatives as below

Q: f: (Z, +) → (Z, +) where f(x) = 2x. f: (R, +) → (R*, .) where f(x) = 2*

A: We will use definition of isomorphism

Q: Find f-(x, y) and fy(x, y). f(1, y) = (y^tan(4x)) fa(x, y) : fo(x, y)

A: The given function is: f(x,y)=y5 tan(4x)-43

Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: