d) | 4f(x)| dæ =

Q: If (5f(x) + 4) dr = 3, then S f(x)dx = %3D

A:

Q: Q4 If f (x, y) = x sin y + ey asf ax2ay3 Find

A: Let's find.

Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: The formulas used in the solution are as follows: 1. Chain rule: df(t)dx=dfdt·dtdx 2. Product rule:…

Q: 2) Prove that: a) dx' dx- b) F) = dF %3D Ldx dx c) [x,p²]= 2h?d/dx

A: To prove- ddx, d2dx2= 0 The mathematical definition of commutators is, A, B= AB-BA Given, L.H.S.…

Q: f tan(z)dz C, = {z € C: -|= 5} CL

A:

Q: dy If 2y = xlnx, then dx (In x)xinx (xinx) In x (b) (d)(In x)xanx) 2

A:

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

A:

Q: 2x-y if F(x, y) = xy é e af ар ay ах find

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: df Compute if f(u) = u?, u(2) = -5, and u'(2) = -5. dx lx=2

A:

Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: fong=メーm X= Sin z0 4= coszo COSzo df =

A:

Q: dy 1. If a? + e 2xy = r + (y-2), find when r 0. dr2

A: We have to find second derivative at x =0.

Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

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Q: H In OJ, GH = 9, KL = 4x + 1. Find x. R 5. 5 S. GK

A: Given: GH=9,KL=4x+1  If from a centre a perpendicular is drawn to the chord, then a chord is divided…

Q: 18. X ve Y bağımsız r.d. ler olsunlar. E(X)=3, E(X²)=25, E(Y)=10, E(Y² )=164 ise Var(3X-Y- 8)=? a.…

A:

Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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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: [d] If xz = yz and z - 0 then x = y

A:

Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

A:

Q: d²y -4 If x? + y? = 4 then show that dx?

A: By simply differentiate  with respect to x to find d^2y/dx^2

Q: af Given f(x, y) = In(7x² + 9y²) then

A:

Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

A:

Q: 21 11 f(x) dæ f(x) dx f(x) dx - 8, where a = and b ...

A: The given integral equation is ∫821fxdx-∫811fxdx=∫abfxdx.

Q: f(z) =z2 is discontinuous in C

A:

Q: (1)F (s)= s +9 2s2 +s -1 %3D

A: Given: L-1s+92s2+s-1

Q: 3- Suppose that s(x)dx 5. Find A- B- S V3 f(2)dz D-

A: Definite Integral of function f(x) in the interval of [1, 2] is 5. The function remains the same for…

Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

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

A: Please see the answer below

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

A: → Use chain rule of differentiation.             ∂(f(g(x)))∂x=∂(f(g(x)))∂(f(x))×∂(f(x))∂x→While…

Q: [₁₁ ) If nd f*. f(x) dx = 4 and g(x) dx = 1, what is the value of ولاء f(x)g(y) dA where D is the…

A:

Q: In the function given. Evaluate the integrals.

A: Given:∫03 fx dx=2,∫36 fx dx=-5∫36 gx dx=1∫36 3 fx -gx dx=?

Q: D. E +xy = axj Solue %3D D

A: Bernoulli's differential equation.

Q: Q3. Find af and at se If f (x, y) = 2e* + Iny2 ,and x = 2t + r2, y = ar r+1

A:

Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

A:

Q: 2. Ex Fnd そ if Z=マ+S+v ノ イ=メS マニメe *S=yさ

A: Given function is, z=r3+s+v2 Where, r=xeys=yexv=x2y

Q: 2. f(x,y) = x5 In(y)

A: Given function is fx,y=x5lny. To find the first and second order partial derivative of the given…

Q: If y = e3x+18 then dx O 4e3x+18 O 3e3x+18 O 54e3x+18 O 18e3¤+18 O 2e3x+18

A: Given that: y = e3x+18

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

A:

Q: 2) Evaluate | xy? dxdy D. where D: x+y² <2, x N 0.

A:

Q: f (x) dx=6, ƒ (x) dx=2, and ƒ (x) dx=- 3, fir If A 4 B

A: We are asked to find the value of given.

Q: d²y d²y If x = f(t) and y = g(t) are twice differentiable then, dx2 di? d²x dt² True False

A: Let x = f(t) and y = g(t)

Q: dy Determine given y = (3u² – 5) if u = V23 dx 5/3

A:

Q: -v-S vdu G) - S -r lee) dx 2 (보라2) 2 (x²t2) - x2 2 (R?+2) ㅜ 2 (x? qz) - (x? $2) z (? t2) In Ix? tz…

A:

Q: 2) f(x)dx= 0.5 by using Simpson's rule with h = 0.5 then b= A 15 B2 CI D 2.5

A: Option c is correct

Q: S-ydx + xd - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O O 2

A: Solution is given below:

Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: find af/àx and af/dy. f(x, y) = x² – xy + y²

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

A:

Q: 3. Jo F(x)dx=-7, S9(xdx= -12, S 9cx) dx - -15 9(X) dx = -15 Find the value a Such that (af(x)…

A:

Q: [f(x)dx, if f(x) = Vx -k+1;k-13x <k,k = 1, 2,..

A: