14 dt t2 – 14t + 50

Q: 4. dr/dt = -2tr, r(0) = ro %3D

A:

Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

Q: 3. 2t t dt ST-t

A: To integrate the given vector function. ∫te2t, t1-t,11-t2dt...(1)

Q: 14. dr/dt = -2tr, r(0) = ro

A: Given query is to find the solution of the differential equation.

Q: 25n Evaluating sec will yield to 6 V3 A 2 2/3 B 3/3 © - 2 V3 D 2.

A:

Q: тахz %3D 2x + у S.t х+у<60 2х + у 2 40 y < 30 х, у 2 0

A: Linear programing is a mathematical techniques to optimize solution of given constraints.

Q: 1 t² dt 4 0.

A:

Q: 2t dt (t + 1)v5t – 7

A: ∫2x2x+15x-7dx Take the constant out:  ∫a·fxdx=a·∫fxdx =2·∫x2x+15x-7dx Substitute u = x+1…

Q: d²r 107. dr? 2. dt 1=1 = 1, r(1) = 1

A: In this question we need to solve the given differential equations.

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A: Integration

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A:

Q: Evaluate using u-subsitutiton?

A: u-substitution means substitute  1-8t=u2. Then solve it.

Q: Evaluste for 2: 0SIS1,0Sy s3. dr dy .

A: The sum rule of exponent states that ap+q=ap·aq. Use the sum rule of exponent to simplify the…

Q: Q.6 Show that: X-1 X+ y – 1(x-1y)= B(x,y)

A: In the given problem we have to show that                                 x-1x+y-1β(x-1,y)=β(x,y)

Q: -2 Evaluate: ²₁² [(x²-²²] du dt x+y

A: We have to find value of given double integral.

Q: 3t 3 dt +C 3lna A) True B) False

A: The given integral is ∫π3tdt=π3t3lnπ+C

Q: 10. dt 1+ 64t2 -1 A) 2sin-1 8 B) C) 2tan-1 D) 2tan-18 A B D.

A: Since you have asked multiple question,As per our policy we will solve the first question for you.…

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A:

Q: dx 7. JIVa² – 2x + 5 (hint: let æ² – 2x + 5 = (z – x)²) -

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

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A:

Q: Find f'cx?, f"cxx) wheve fcK) = xe -2 Jc %3D

A:

Q: Q2: Consider the IVP: y=1+2,1sıs2, y(1)=2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: dr 19. 1/2 23 de 21. (2-z 2) dr 22. t 1/2 dt 27 t +1 dt 23.

A:

Q: 6/11 - 8) AT= 12 RT = 4x S. T %3D doesn't R

A: Given: A parallelogram STQR. As per the property of parallelogram, the diagonals bisect each other.…

Q: c) cosh(2 + j3) d) csch 1 + j (₁ + ; ²7/1) 3.

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Q: 27" + 4y = t Yo) =1, y'c0) = 2 %3D %3D

A:

Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

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Q: iii) ä(t) – 9x(t) = 0, x(0) = 1, ±(0) = 0 -

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Q: Q2: Prove that: d 1 csc dx c-1(Invx) 2x- |Inv(Invx)* -1

A: Here we need to find the derivative of given function. We will use chain rule of differentiation.

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: If ∫01f(t)dt=11, what is ∫00.25f(1−4t)dt? ∫11.5f(3−2t)dt?

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Q: I(n) = ;n² - 글까-10 5-2t h(t) = t- 1 %3D S(h(0.5)) =

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Q: 2₁ "+21y+8x=y" + 5y' + ex

A:

Q: 130. у — In (r² + 1) dt

A: We have to find the integration

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Q: u? – 1 du J2x u² + 1 3x - 56. g(x) :

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Q: 3 Q 4. Differentiate Vx2 Vx2 2 +

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Q: Q2(a). Evaluate 1 t4+9 dt 0 t4+9t2

A: solution is given below

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Q: Evaluate the integrals

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Q: 7) t(2w – t + 1)dw + w(3w – 4t + 3)dt = 0, when t(1) =-1

A: Given differential equation  t(2w-t+1)dw+w(3w-4t+3)dt=0  , when  t(1)=-1

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A:

Q: AJKL-AABC AKLR ATSR J. K (5y) 2x-4 24 21 64 K T. 24 5x-4 S. A. 64 6y- 12 14 50% 30 B R. 11. x = 13.…

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Q: 11. (16D³ + 12D²2 – 1)y = 0 ; y(0) = 1, y'(0) = 0, y"(0) = –1

A: