Ir If z = f(x- y), then of df дх ду 1 -1 12 O 5

Q: 2+i (a) Evaluate dz , along the line x=2y.

A:

Q: c1 f(x, y) dy da = F(z, 9) dz dy %3D O True O False

A:

Q: iF w=f(x-y₁ y-Z, Z-x) then dw dw dw = ? dx dy dz Chain roll

A: Chain Rule : If w= f(a,b,c) and a=g(x,y,z) ; b= h(x,y,z) and c= l(x,y,z) then…

Q: X,X, X3 R.S. T3 %3D Bind dis tribution of Xo

A: Solution

Q: H.W: Find f, f, and f, if f(x, y, z)= x - √y² + z² x=(x.x)\S xh + lis

A: Here we have to use the concept of partial derivatives

Q: ["[" f(2,3) dy dr True False [1 f(x, y) de dy

A:

Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

A:

Q: If f(x, y) = cos(æ – 4y) then: fea(x, y) = fay(x, y) = fw (x, y) =

A: The function is f(x, y) = cos(x - 4y)

Q: If F(s) = 1/(S-2), then f(t) is %3D a) e²'u(t) c) u(t-2) d) e"'u(t) -2t b) u(t +2)

A: Given Fs=1s−2 We have to find the ft Use definition of inverse Laplace transform, which is given…

Q: f(x, y) = (-x – 2y, x – 4y).

A: Follow the steps.

Q: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

A:

Q: If f(x,y,z) = In(xz) – 2xy²z, find fzxy at the point ( 0.5, 1,-1) %3D a) b) - 1 c) 8 d) – 2 e) - 4…

A:

Q: dw and ds dw Assume that w = f(s³ +r?) and f'(x) = e*. Find dw dw ds II

A: Partial derivative

Q: f (u, v, w) can be differentiated and if u = x-y, v = y-z, w = (z-x) ôf of ôf + + ду дг

A: Since is a function of and they are described as, Thus, we can say that is a composite…

Q: Evaluate (F JC Er F • dr. F(x, y) = xi + yj C: r(t) = (7t + 4)i + tj, 0≤t≤1

A:

Q: F(x, y) = yi – xj

A:

Q: dw 3. If w = f(x, y, z), g(x, y) = C₁, h(x, z) = C₂ find: dx constants. c1& c2 are

A:

Q: f(2) — и(х, у) + jo(x, y) и(х, у) — е% сos x — х f (0) = 1

A:

Q: If f (x, y) = x²y? + sin(ry), then fy (2,0) =

A: Given function is fx,y=x2y2+sinxy. To find: fy2,0 Solution: Partial derivative of a multi-variables…

Q: 24. If f(x, y)=x²y+cosy+ ysinx, find fu, fyy & fry.

A:

Q: af af a²f 1. Given f(x, y) = x' + y* find ax ' dy' dxdy and - дудх

A: Please see the answer below

Q: Let f(x,y) = In (x³y). If fx(6,2)=fy(5,a) what is the value of a? а. 1 O b.-1 O C. 0 O d. 2 O e. -2

A:

Q: 04|| Find ôw/ôr and ôw/ôs as function of r and s, if: w = 2x + 3y² + 4z, X =r + s, y= cos (r - s), z…

A: Given   ω=2x+3y2+4z   x=r+s   y=cos r-s   z=erNow,      ∂ω∂r=∂ω∂x.∂x∂r+∂ω∂y.∂y∂r+∂ω∂z.∂z∂r→       1…

Q: х%3D1, 2, 3, Let f(x)= - otherwise a. Find G,(t). b. Use G,(t) to find V(X).

A: The probability mass function of X is, (a) The value of is,               Therefore,

Q: 10 f(z) dz - f(z) dz f(z) dz where a = and b:

A:

Q: If f(x,y,z) = In(xz) – 2xy2z, find fzxy at the point (0.5, 1,-1) %3D a) b) - 1 c) 8 d) – 2 e) - 4 g)…

A: We use the definition of partial derivatives to find the solution of the given question.

Q: b. f:R² → R defined by f(x, y) = x² + y². Find f-1(0), f-'(1), and f-1(U), where U = (1,4). %3D %3D

A: Given data:     The expression of the function is: f(x,y)=x2+y2.     The expression for the inverse…

Q: 6 X, 一T Sx< 0, 10, f(x) = %3D f(x+27) = f(x) 0 <x < T;

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: g(x)]dx, (b> a), for all f, g € X. Show that (X, d) is a me

A: Matric Space

Q: 2+i (a) Evaluate [z dz , along the line x=2y. 1

A: Since you mention to solve only part a therefore I will solve only (a)

Q: x2 If w = x".f then show that: + y², X. Wx + y. wy = nw.

A:

Q: f(x, y) %3D 3ху + у? (а) f(x + Дх, у) f(x, у + Ду) — f(x, у) - (b) Ду Зх + 2y + Ду Ду # 0

A:

Q: 1 Vf(x,y)

A: Given f(x,y)=ln yWe know that ddx(ln x)=1x

Q: Let I:=∬DydA, where D={(x,y): y≤x≤4, 0≤y≤1}.  The value of I is?

A:

Q: eſt 2 du given that * f(z) dx = 12 f(4Tan¹(u)) 1+u² Evaluate

A: Hint :  This problem is application method of substitution in definite integral. If you have not…

Q: 14. F(t) = 27,0st<3; F(t + 3) = F(t) %3D %3D 15. F(t) = {.0<t< 4

A: Note : " As per our guidelines we will solve the  first question . If you want any specific question…

Q: ax +b. N<2 Given fx) - find a & b such that f is differentiable at 2. 1212-1, x22

A:

Q: If f(x, y) = xe"y – In(xy), then dxðy Select one: A. x² ye"Y + 2xe" B. x² ye®y – 2xe™y С. О D. x²…

A: f(x,y)=xexy-ln(xy)

Q: س/ أختار قيمة R ,D المناسبة ل لداله الاتية f(x) = 2 + Vx? - 1 Df = {x:xeR:x 0} O الخيار رقم 1 D, =…

A: The given function is fx=2+x2-1. Calculate the domain and range. Range is defined the all possible…

Q: Q.42 (So f'(z)dz)' fo (f(z))'dz If f(0) = 0 and f'(z) = (0, 1]vz = [0, 1] then- can not take values

A:

Q: Jx + 1 if x is even b. f(x) = S = {0, 1, 5, 9}, T = Z – E if x is odd; 2 7 11

A: The given function isfx=x+1if x is evenxif x is oddS=0, 1, 5, 9T=ℤ-Ewhere ℤ is the set of integers…

Q: af af Find and ds z when f(x, y) = e*cosy, x= 2s - f and y= 3st. af

A: Given problem:-

Q: f(x)= { (X-1), 16X <3 O ; elowhe re Uenity that f oo a- b. find P(I Cx sa) <X sa) puy .9

A: Introduction: The probability density function of a continuous random variable, integrated over the…

Q: If f(x,y,z) = In(xz) - 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D -3 d) – 2 e) - 4 g) None…

A: ANSWER

Q: af Find if f(x,y) = y sin xy ax %3D

A:

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

A: We will use definition of isomorphism

Q: (a) || f(x,y) dA = L f(x, 9) dyda + 1 f(2, 4) dydr R (b) || f(x,y) dA f(x, y) dædy R (2, 3) (5, 3)…

A: We need to write the limits accoding to x and y asix.

Q: [D] Evaluate det (A), where 0 0 a u b 0 A = v w с 0 2 d

A: Let's find.

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);…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.