Using Boole's Rule, Evaluate (x² + 3y²)dxdy

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:…

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A: The question is taken from the partial derivative in which we have to find the derivative of the…

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Q: Given f(x, y) = 12/8x* + 6y + 2xy°, find f. (x, y) = f,(x, y) =

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Q: af If f(x, y)= 3xy+5y, then О а. a. 3x e O b. 3xy OC 6x c. Od 6x)

A: c. 6x is correct.

Q: sy? is a real part z = x+ iy is a ce action v is

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Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: using Runge xy' = y lnx, y(2) = e in the domain of [2,4], also find y(2.8), y(3.6).

A: Given, xy'=ylnx   , y2=e in the domain of 2,4

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Q: af Find the values at the point (-7, 3) if and dy 3 S(x, y) = 32x° + 5x²y" + y} – -

A: fx, y=3x5+5x2y3+y23-37 Differentiating wrt x, we get  fxx, y=15x4+10xy3⇒fx-7, 3=15-74+10-733fx-7,…

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Q: Find fx, fy, f₂. fx = f(x,y,z)=x-√√√²+z² (Type an exact answer, using radicals as needed.)

A: The given function is fx,y,x=x-y2+z2. We have to find fx,fy and fz.

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

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Q: Using the coffee demand function, Q = 8.56 − p − 0.3ps + 0.1Y, show that sugar is a complement for…

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A: Here to use implicit diffrentiation method for solving the problem

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Q: dx first using a trig substitution and then using a standard substitution. x²+36 Find f

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Q: O Evaluate, (a) / 3y* In (y) dy

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Q: B) Find real numbers x, y, z for the identity below 2xi + 2yj- 2i + 3j + 2k = 3i -j+ zk

A: (2x-2)i+(2y+3)j+2k=3i-j+zk On comparing both sides

Q: af Find the ar I and iff (x,y) = x² - xy, x = r² + s and y =r - s² as

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Q: Exercise: Write the order an d²y dx² + a²x = 0 1-

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

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Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 J = exp(-x²)dx = Se

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Q: To find ∫x3(x4−15)7dx∫x3(x4−15)7dx, you would need to use u-substitution. What u could be used to…

A: ∫x3(x4-15)7dx

Q: Using the Method of Substitution, evaluate : 54х dx (1 – x2 O 54 /1 – x² + C, Where C is the…

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Q: dx Evaluate using trig substitution: a x'V4-x? upo an

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Q: ☺ using the definition f'sx) = li fCxth)-fx) find f'(x) when fex) %3D 2x-3

A: The given function,    f(x)=72x-3

Q: Let g(u) = [" dx. Then dg 3 2+x2 du

A: The given integral is gu=∫3u312+x2dx. By applying the Fundamental Theorem of calculus,…

Q: は F-R m Show that u is 3. sauomphic to F

A: V is isomorphic to F3 means  There is a bijection map between V to F3 such that that bijection is…

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

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Q: xy Let z . Then: 4x2 – 5y? | az dz ду

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Q: af , Given the function f (x,y) = 3x – x²y² + 2x°y, what is iTe ду А. 3 — 2ху? + бх?у В. - 2х3у +…

A: Given query is to find the partial derivative with respect to y.

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A: we have to find f'x

Q: (a) Use the defin this section to fim f'(x) = (b) Find the insta

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A: Given F is a null set, i.e. F=∅ We need to find the arbitrary union of null set, i.e. ∪F

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Q: d Q3/ By using definition, proof that cot x = – csc² x . dx |

A: Derivative of cotx with respect to x is csc2x.