16. Use f(x) = 2x and g(x) = to evaluate the exp %3D a. (fo g)(2) b. (g o f)(- 7)

Q: Find e* + x-2 + C e* – 1+ C + C (1/2)x² e* – In |x| + C

A:

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

A:

Q: Evaluate the given function using homogeneous x- yArctan () dx + xArctan () dy = 0 A. 2yArctan ()…

A: We need to find solution of differential equation using homogenous.

Q: 12. f(x, y) = x' – 2x – y + 4y, P = (1, 2). -

A:

Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: Calculate ∂ω/∂x for ω=e^−2x x(multiplied by) e^(z^2y)

A:

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: 3. Is the function y = Cx² a solution to the ODE y" – xy' + y = 0?

A: Solution is given as below:

Q: ー2 f Cx.y)=In Cx Zp

A: Please refer to the image below

Q: Find for following 1.y = (x + v3x)S

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: [g(x )cx = 2 If then g(x )dx equals

A:

Q: 4 + 8x is x2 The antiderivative of the function f(x) = %3D

A:

Q: dæ Evaluate: x/9x² +4 A) None of the above V9x² + 4 + 2 B f (x) = -2 ln +C %3D 3x © s(12) = -- In f…

A: I=∫dxx9x2+49x2+4=t9x  dx9x2+4=dtdx=9x2+49x dtI=∫19x2 duI=∫1u2-4 duI=∫1(u-2)(u+2)…

Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

A:

Q: f(x)=x²-2x Sf(x)dx using four subintervals by on Estimate -1 d M4.

A: Given function is We divide the interval [-1,1] into four sub-intervals with length of each is…

Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

A:

Q: 2 Find the general antiderivative of f(x) = 5x* + 4 + C

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: 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: 1. Find the relative maxima and minima of y by the second-derivative test: (a) y = --2x? + 8x + 25…

A: Consider the provided question, According to you we have to solve the part (b), (c) and (d). (b)

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: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

A:

Q: let y(1) = 1/e and xy'-y+y^2*e^x = 0   calculate the smallest of the values ​​of x in the y domain

A: Let us consider the Bernoulli equation y'+P(x)y=Q(x)yn To convert the  equation into standard form…

Q: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

Q: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis

A:

Q: If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

A: In this question we have to compute kf(1).

Q: O For the bvp d²y - 9y = 3x, y(0) = y(1) = 0 the Green's functions G(x, §) satisfies d²G(x,£) -…

A: The greens function satisfies the homogeneous differential equation, not the non - homogeneous…

Q: Consider the following IVP: y' = e; y(0) = 2

A:

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

A:

Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

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

A:

Q: Q3: if f(x)= xy+2x-5y =2 then =dy/dx (x-xy^2)/(x^2 y-y) O (x-y)/(x^2 y) (x^2-xy^2)/(xy-y) O

A:

Q: 9 2. If fS(x)dx= 37 and g(x)dx=16, = 16, find [2f(x)+3g(x) ]dx- %3D 0.

A:

Q: Calculate ∂ω/∂z for ω=e -2xe((z^2)y)

A: While calculating partial derivative ∂ω/∂z, all other variable except z will be considered as…

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

A:

Q: (14) f (x,y)=e" (x² +y²)

A: f(x,y) = (x^2+y^2)e^-y fx= 2xe^-y fy= -(e^-y)(x^2+y^2)+ 2ye^-y fxx = 2e^-y fyy = (e^-y)(x^2+y^2)…

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: (b) If g(x) = [,! 1 dt, find g'(x) 4+t2

A:

Q: Í (x)dx, iff(x) = Vx -k +1;k-15x <k, k = 1, 2,.n.

A:

Q: 16. If x x y and y x z, then how is x proportionally related to z?

A:

Q: (c) f(z) = -I Vr E |-1,.

A:

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

A:

Q: If (a,B) is a saddle point of the function f(x,y)=27y2-y3+3x²-6xy, then a+ß=

A:

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: Does y =e9-x2-2 exist?

A: Given an equation, y=e9-x2-2. To check whether the equation exists or not. The value of e is…

Q: If (a,B) is a saddle point of the function f(x,y)=21y2-y3+3x2-6xy, then a+ß=

A:

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

A:

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

A: