а. f(x) %3D Vx + 15 b. g(x) = Vx + 15 – 2 с. К(х) Vx + 15 – 2 -

Q: y= cosV1- x y' = V1-x² ² y' = 2v1- x² y' = 2va- x2 y' = Vx-x* 1 y' = 2Vx-x2

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Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

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Q: 7. Differentiate a) f(x) = ev==t and b) h(x)= (5x² – 8r)e**-4". %3D

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Q: 5.Find f, L L*(x² + y² )dydxdz

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Q: 9. y = x – 5x+52) 21n10. y = 2r2 11. f(x) = 12. f(x) %3D x² +x- 6 15x2 +31x + 1 13

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

Q: 5T 1 y=-2cos(Gx+っ)+1

A: Phase shift: -5π

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: Find y' by implicit dif ferentiation for 2y³+4x² –y = x6 . 6x5- 8x y '=- 6y2 – 1 A 6r5 + 8x B 6y2– 1…

A: Given, 2y3+4x2-y =x6 We have to find y' by using the implicit differentiation.

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

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Q: Find the general solution of (T^2 + 4)y' + 2ty = t^2 (t^2 + 4) with the variation of parameters…

A: In this question, we find the general solution of (t2+4)y'+2ty=t2(t2+4) with the variation of…

Q: a) Y= ezx-e-zx €²x+e-2x

A: Given,   y=e2x-e-2xe2x+e-2x

Q: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

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Q: 6 - 3x2 + 3 Find the general antiderivative of f(x) - - - x5 + C

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Q: d. yı = X1 X3 X1 + X2 Ya = - X1 – 3x2 – 2x3 e. yı = x1 + 2x2 + X3 Y2 = Y2 = x1 + x2 Ya = X2 + X3.

A: d)  The map from R3 to R2 is onto.  e)   The map from R3 to R3 is not onto.

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: Differentiate y = In(x³ + e*) .2 3x+eX А. x3+e-X 3x2-ex В. x3 +e-X 3x2-e-x C. x3-e-X 3x2-e-x D.…

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Q: z· 3°dz

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

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Q: y" - 2y' + 2y = e'cscx

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Q: -x-3 F(x) = S (5t + 2) dt

A: According to question given thatF(x)=∫x3x-35t+2 dt

Q: t² - t dt 0, = (x)6 g'(4) =

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Q: 8. fz/25 – z² dz

A: Consider the provided integral, ∫z225-z2dz Evaluate the provided integral. Apply the method of…

Q: (b) Differentiate (Vx+ 1) with respect to x. 2/3

A: as per our guideline we can solve maximum one question you can repost other questions

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: y' +(E- 1)y ==

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Q: .3 S(3 – e3*)²dx

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Q: 3 V9-y s S f(1,y)dxdy. y)dzdy. y-3

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Q: S2-3x', x>2 Vx -2, х <2 а) g(x)-

A: The given function is gx=2-3x3,   x&gt;2x-2,    x≤2. Sketch the graph of this function as shown…

Q: px + qy=z-a √x² + y² + z²

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Q: S sec 2ydy

A: Topic:- integration

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: Derivatives of the sum of functions Find the derivative of thefollowing functions

A: We have to find the derivatives of following functions: 19. fx=3x4+7x20. gx=6x5-x21. fx=10x4-32x+12…

Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

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Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

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

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Q: 4. Suppose y = 3x + 2. What is Ay if x increases by 3?

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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: Vy² – 25 dy y3

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Q2/ By using partial method solve fx² In x dx

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Q: Find (5x - x²)e* dx O(x2 -5x)e-x-(2x - 5)e¯X – 2e-*+c O (5x-x2)e*- (5 – 2x)e* +2e* O (x2-5x)e*- (2x…

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Q: (Sx-8)3 12. g(x) = (*+3) 13. g(x) =. _(x²-s}' 14. y= 2x 15. J09=

A: Dear student,                    According to our guidelines we can answer only first question or…

Q: dy 6. S: y3-2y2

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Q: 4. V21+4:-z dz

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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: 4. Solve y"- 4y' +3y = 1 by variation of parameters. %3D 1+e-*

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Q: /25-22-y2 zVx² + y? + z² dz dy dr

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Q: f(x) = é ーx46x? J6-6x -6 A) e-+6z² (-6x³ + 12x) + 2/6 – 6x Calculate f (x) 1 2/6 – 6x B) e-+6z°…

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Q: (b) Evaluate |(2x+3)V x² + 3x – 5 dx , by using substitution method.

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