b). f(x) = (2x + 1)³, a e R

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

A:

Q: 5.Find f, L L*(x² + y² )dydxdz

A:

Q: If f(x,y)=xe"*/2+135x?y3, then əx²əy³ at (1,1) is equal to

A:

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: (e) x²y "+xy '- y = 1+x

A:

Q: 3 5) Differentiate with respect to x: y = %3D 3x e

A: Solving the problem by finding the differentiation.

Q: 5 2 11 what is 3 Given that f(æ)dæ : f(s)ds?

A: We will use the following 2 properties of definite integrals to find the answer

Q: Solve the DE f'(x) = 5x given that f(0) = 3. %3D A y +3

A:

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

A:

Q: , y = X = t+2 t+2,

A: The solution of the problem is given in the next step.

Q: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: Find dy for the given values of x and ∆x. ; y = 2x3 + x2 - 4x; x = 2, ∆x = -0.2

A: Find dy for the given values of x and ∆x.

Q: f (x) = x³ – 23 6x + 1. | e sure to verify the c

A:

Q: f(z, 9) = 82" + 5y² + 4z°y+ e7=y of Calculate

A:

Q: If xy2 3x2y + C, then what is the value of C at (2,2)?

A:

Q: 1. f (x, y) = x² + y?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Se-2t if 0 3,

A:

Q: (e) f(x1,x2) = xỉ/x2 on R x R++.

A: The solution of (e) is in below

Q: 33. f(x, y) = xr – 3xy² + 6y²

A:

Q: What is the particular eq. of the given:   y"-3y'+2y= xe^x +1

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliary…

Q: f(x,y) = (x³ − x)(x² − 1). find fxy(x, ×

A: We have given that ,  fx , y = x3 - x y2 - 1 We need to find , Partial derivative fxy . We know that…

Q: 2 The Range (Ry) of y = v9 – x² -

A:

Q: j. f'(2) appears to have a value of

A:

Q: Evaluate the Cauchy principal value of 2x² - 1 fo dx. x4 + 5x² + 4

A:

Q: Q3: if f(x)= xy+2x-5y =2 then dy/dx3D a- b- C-

A: We know that dy/dx mean difernciate f(x) with x. From this we will get our answer.

Q: Suppose that 4x² + 2y² = t² and y=tsin 0. Find ду (27) ət 0 and at ?x

A: The given equation is y=t sin θ. Consider sin θ is a constant term.

Q: [E (XY)P SE (X²) E (Y²)

A:

Q: b) f(x, y)=-2x². + 8x − 3y² + 24y + 7

A:

Q: y = v1 - x2 from a = 0 to r = ;

A:

Q: 2. Verify the following derivatives : d а) dx 45x +(Vx + b) 4Vx(ax² + bx +c)]=,_ d 1 -(5ax² + 3bx +…

A:

Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: Solve the equation using Reduction of Order y" -y = 2et Oy=c₁e¹ + c₂xet + e* (x + c3e-²x + C4)…

A:

Q: 2x2 f' (æ) = If f(x) = V 1+t° dt, then

A: To find the derivative of integral apply the follow rule

Q: I Findk the GS op the bE (x+3y)kk +(3x+g-) dy mo 50

A:

Q: Q3: 1f f (x,y) = 6x*y5 + 4x*y4 Prove that: f (x,y) * fxxyy fxx * fyy = 1

A:

Q: (d) If g(x) = Vx + 1, derive g-(y). %3D

A:

Q: E. y = xArctanx - In V1+x

A:

Q: -2 The domain of f(x,y) = is %3D x² + y?

A: f(x,y)=-2x2+y2

Q: f Lan 2X e *3 of +sec2X Pinel dy o

A:

Q: 4) Aşağıdaki fonksiyonlardan hangileri a2 əx² 1 a2 v² ət²! dx2 dalga denklemini sağlar? Neden? a) f…

A: a) Given that f=5x-5vt3 Now, differentiating f with respect to x, we get  ∂f∂x=35x-5vt25=155x-5vt2…

Q: 41 82x-x2 9V x²+y? dydx =

A:

Q: Find d²y/dx2 for the followi f) x2/3 + y2/3 = 1 %3D ³ g) x + y = 16

A:

Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

A:

Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

A:

Q: Solve for fxx, fxy, fyx and fyy given f(x, y) = 2 ln(x − y).

A: The given function is:fx,y=2 lnx-y.We need find fxx, fxy, fyx and fyy

Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-

Q: 7 If f(x, y) = (3x³ + 2y² – 30)', then fy is - given by :

A:

Q: (b) f(z)= (4 – 5e*)³ x² + 1 (c) f(r)= ez %3D (d) f(z) = e=²–5z+4 ez-5x+4 (e) f(x)=xe² – e² = re² –…

A: We can solve this as follows: