Q3 Given that w = x + 2y + z²,x = = ,y = r2 + In s, z = 2r X%3D %3D aw aw and ar Find as

Q: So S zy dy dx 4 c2 1 Show all steps to evaluate by hand: Vx 2y3+1

A: We have to evaluate the integral                                                    ∫04∫x212y3+1dydx

Q: 8. If JM = x+ 17 and MK = 5x – 23, find JL. %3D J M 'K

A: 8 .          J M = x +17           MK =5X -23          Since  JM = MK        ⇒ x + 17 = 5x -23…

Q: It is given that dn (Inx %3D anlnx+bn where an and bn depend only on n. dxn xn+1 Find a1, az and a3.

A: we have to derivate three times then we will get a_2,a_2,a_3

Q: Find the most general antiderivative. 4t dt O A. 12t° + 6. O B. +t+C O C. 8t++C OD. +C 18 2/9

A:

Q: (2) = [| (a) %3D h (b) Value(s) that are NOT in the domain of -

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Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. У'%3…

A:

Q: (r+6)dr 4. S (z+2)?

A: Given: = The indefinite integral is, ∫(x+6)(x+2)2dx To find: -The complete solution of the given…

Q: JK = 4x + 8, %3D KL = 5x + 6, and JL = 86, %3D Find KL. J K L

A:

Q: Given dy dy dz² +2 + 5y = e dr and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the…

A:

Q: Given : S 6x³e**+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv =…

A:

Q: 3. y = 1+Vx eğrisi, y = 3 – x doğrusu ve eksenler arasında kalan bölgenin koordinat düzleminin 1.…

A: Given the curve y=1+x, and the line y=3-x. Find the area between the curve, line  and bounded by the…

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value.…

A:

Q: Given : 6x³e** +3 dx. Using integration by parts (S udv = uv - f vdu) and letting u = f(x), dv =…

A: Given,           ∫6x3ex2+3dx

Q: That is *z' in the given Bernoulli DE (6xy³ - y)dx + 2x²dy = 0? lect the correct response: O -y-2 y2…

A: Rewriting it, dydx=-(6xy3-y)2x2dydx=-3y3x+y2x2thus we have,dydx-y2x2=-3xy3

Q: Given : S 6x³e**3 dx. Using integration by parts (S udv = uv – dv = 3g(x)dx find h(x) if ſ vdu =…

A: Let's find.

Q: SSS 12z dV E where E is enclosed by z = x? + y² and z = 1 О Зл O 27 O 4T O JT

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. у'3D…

A:

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: Given that S" 4Væ dx = 152, what is fo*4Vt dt ? 3 )

A: As we know that;  the value of definite integral will not change if independent variables changes,…

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value.…

A:

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: 34. Which of the following is solvable directly by power rule of antiderivative? A. [xe"dx B. Ssin*…

A: Which of the following is solvable directly by power rule of antiderivative?

Q: For the given DE with coefticients linear in two variables, do the following: (x - 2y)dx + (2x…

A:

Q: Q2] Classify the following D.E to: order, degree, homogeneous, and linear: dy 2y=x 3 dx dx

A: We can solve this as follows:

Q: Given : S 6x³e**+3 dx. Using integration by parts (S udv = uv - fvdu) and letting u = f(x), dv =…

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. y' =…

A: We have first order differential equation and to slove this use Runge kutta 4 order method. Given…

Q: Q 4. a) Use integration by parts to evaluate Sz²cos zdz. b) Evaluate f xlog(x + 3)dx.

A:

Q: Use RK2 (Heun's method) with ħ = 0.5 to estimate y(1) given o: 8 Vū, y(t = 0) = 8, y' (t = 0) = 2.…

A: The Heun's method formula is The given values are h=0.5, y(0)=8, y'(0)=2 That is x0=0,y0=8 and…

Q: Given : S 6x³e*+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv =…

A:

Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: 1. Find the saution YLEA oR Ele tntifial Value poobem y"-8y'+16y=8e*, yr0)=3,4'101=2,

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Q: Suppose that n # 0 and n # 1. Show that the sub- stitution v = y!-" transforms the Bernoulli…

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Q: 8. If JM = x + 17 and MK = 5x – 23, find JL. %3D H. 'K

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: Find nalytical salution to Pnti = (r+)+m possible. an Simplity as much as

A: Given equation is: Pn+1=r+1Pn+m⇒Pn+1=rPn+Pn+m⇒Pn+1-rPn-Pn=m

Q: Evaluate SSS 12z dV E where E is enclosed by z = x? + y? and z = 1

A:

Q: Find a positive value of k for which y=sin⁡(kt) satisfies d2y/dt2+16y=0.   k=

A: Double derivative

Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

A:

Q: Given: J6x e* dx, Using integration by parts Suov= u= f(x), dv= 3 g(x) dx, find h(x) if |vdu = h(x)…

A: to find:- h(x).

Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

A:

Q: dx 4V3 – 7t x(9) = 8. %3D %3D %3D dt

A: Finding x from the given conditions.

Q: Find the general solution to dw ol Sa'(t) = x(t) – y(t) + 3e'; ly'(t) = y(t) – x(t) + 2e'; (8) (8)…

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Q: The antiderivative of [Vx-25 dx is V x2 - 25 - sec-x+ C. A True B False

A: Given: I=∫x2-25xdx     As we know from the trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation

Q: e obtained by r

A: