6. Extended substitution 7. The split method (x+3)- Vx+1 dx 2x+8 x+6x+13

Q: 2. O Differantiate each of foll. funchions- fox) メん fa)= d 2X (42) 2-1 2. Ans 2.

A:

Q: y = VI(1 – 1) 1 y = (z+5a) (++5x) 1

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2x2 ノ ーイ<xLO X 16 X pected vabe of the flx) = り2Xと2 what is e vari able

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Q: 6x + 16y af If f(1, y) then is : 6x 16y ду

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Q: L1:x = 3 - t, y = 4 + 3t , z = -1+ 2t %3D L2: x = -2 + 3s, y = 3 – 2s, z = 3s %3D

A:

Q: 10 10 10 f(x) dx = 31 and [4f(x) + 6g(x)] dx. If д(x) dx %3D 14, find

A:

Q: 5-4y2 dy 3+2y

A: To evaluate ∫5-4y23+2ydy

Q: Find ƒx (x, y)  and ƒy( x, y) .

A: Differentiate the function f(x,y)=ln|2x2+y2| with respect to x and keeping y as constant and carry…

Q: nclosed by x = y, x = 2 - y and the x-axis?

A: And: 5/6

Q: x' = 2x + 3y – z y' = x + z z'%3D 4х — 2у + 62

A:

Q: (3x2 - 2ху+ 3у?)аx%3D 4ху dy O (y- x)³(v+3x) = Cx³ O (v +3x)°(y- x)= Cx³ O (y-3x)°ly+ x) = Cx² O…

A:

Q: Use separation of variables to find a product solution to the following: д н ди -u=1.k>0 дх2 дг

A:

Q: ス+)V2x+x dxメ

A: Given,          ∫x+12x+x2dx

Q: 4. y = vx +2 %3D x,for - 2 < x< 2 2, for x22 (x-1,for x< -2 5. y=

A: To sketch the graph of the given function and determine the domain and range.

Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

A:

Q: SWZ-VX WZ +Vx)³ dx = Select one: а. 금 (x-2)6 + c b. -2 글(x-2)6+ c C. -5 (x-2)6 + c d.

A:

Q: B2. Evaluate (x? V1+x dx by using substitution method.

A: Integration

Q: 13. f(x, y) = x³ – y³ – 2xy + 6 %3D

A:

Q: 2. f(x,y)= 2x + 6xy +y

A: Partial derivative

Q: 19. x' = -2y, y' = 2x; x(0) = 1, y(0) = 0 %3D

A:

Q: 2(x-1) + If y = Vx? – 2x then y' %3D | 3Vx2-2x

A: To find the derivative of the given y

Q: evaluate using the appropriate method or combination of methods.

A:

Q: 5. y = xArctanx - In VI+x

A:

Q: 10 Let y = ( 2x + Then -A(2x + 10)" (2- 10)°, dy = A[ 2x + 2 - where A = %3D C = %3D

A:

Q: 3. f(x,y) = x³sin (2) %3D

A: We will find out the required value.

Q: af If 2xy(-x² + y) + xe", what is ду ду? Select one: а. 4ху — 2x3 + хеУ ду? 2x(-x² + 1) + xe" b. ду?…

A: Given ∂f∂y=2xy−x2+y+xey

Q: 16. Using integration by parts to solve 2√4x²+k A. -√4-x² + k √4x²+k -2√4x²+k B. C. x³ dx √4-x² and…

A: Given: ∫x3dx4-x2

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: (3) Let X = n(µ,4) and Var(2x) = E(4–7x) find µ. %3D

A:

Q: he equilibrium pul 12) P(x) = -2x + 8, S(x) = 3x + 2 %3D

A:

Q: rcosck) X)= 2メ+ hca) + ě Uf)→ at メ=3 @ fiw) = O (fuda (x)

A:

Q: 6. 6. If f(x) dx = 37 and g(x) dx = %3D 16, find [3f(x) + 4g(x)] dx.

A: Given that                                           we have to find…

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

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Q: 2 da x² – 8x + 17 Integrate: + C

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Q: What value of c will satisfy y(x) = c(1 – x²) given y(2) = 1 ? %3D ) Option 1 Option 2 2.

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Q: 5. y = XArctanx - In Vi+x

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Q: Lion 1-y If x = Show that 1+y dy V1-y

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Q: .7 f(x)dx= 12 and f(x)dx = 3.1, then 5. If %3D

A:

Q: Зх-1 4x+2' , find a) R , and b) R(x+h)-R(x) x+2, 3. Given R(x) = E) %3D

A: Given: R(x)=3x-14x+2

Q: Evaluate V1-x-dx A. --(x+xvI– x-) +C B. (x+xV1%3=x) +C c. (x+xv1+x-) +C D. -(x-xVT-x-) + C xv1-x)+ C

A: Find your answer below

Q: find the first and second derivativ of y with respect to x y=x^3-9x^2+15x-5

A: Given:       y=x3-9x2+15x-5 First derivative:     differentiating with respect to x.…

Q: A. Using the basic formulas, integrate the following: 1. fx(x² +2)²dx 2. S(2V – 3x)²dx 3. fx³Vxdx 4.…

A: Note: As per our guidelines we are supposed to answer only 3 sub parts under one question. kindly…

Q: 8 If f(x) dx = 37 and g(x) dx = 12, find %3D [2f(x) + 4g(x)] dx.

A: Given ∫08f(x)dx=37 and ∫08g(x)dx=12We have to find ∫08(2f(x)+4g(x))dx

Q: 7. The split method 2x+8 dx x´ +6x+13

A: to calculate the given integral

Q: X (2x +1) ax wing u- technique

A: To evaluate the integral: ∫x2x+12 dx Solution: Integration by parts states that: ∫uv dx=u∫v dx-∫u'∫v…

Q: 5. If x-2ry+ 3y² = 8, then dx %3D 8+ 2y -2x (A) 6y-2x Зу - х (В) y-x (C) 113

A:

Q: Let X = n(µ,4) and Var(2x) = E(4–7x) find %3D H.

A: Given: a random variable X follows normal distribution. Mathematically, X~N(μ,4) The expected value…

Q: S(3x².fu)+x°, f'(x) dx =24 so, so, f(2) = ) %3D

A: We have to solve the given question. Derivative of the function f(x) can be written as f'(x) Product…

Q: х+ 2y < 12 —х + у s 5 x+у < 5 х2 0, у 2 0. p = (х, у) %3D

A:

Q: seParable 5い / / とll y=2メJタ! 4 xx

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.