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Q: 1 2 [² [²² xe*+5%dydæ 0 0 Write your answer in exact form. Find

A: Here we have to compute the given integral.

Q: 5 4) L-1 s² + 2s – 3

A: First break into partial form then use in verse laplace

Q: QUESTION 1 Please show work NEATLY

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Q: 2) 4 ft V = (4/3) * * %3D TC V = (4/3) * n * V = (4/3) * n * O V ) feet

A: We have to find volume

Q: S(x + 1)(2 – x)° dx 7(2 - x)* - (2 - x)* +c 7(2 - x)* -(2 – x)* +c 3. (2 - x)* +(2 – x)* +c 금(2-x)*…

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Q: What is the last term in the expansion (2xy z+3x²y)4?

A: Consider the provided expression, 2xy2z3+3x2y4 Write the last term of the expression. Apply the…

Q: √__(x+1) dx (x+2)(x-1)² 1 9 3 2 0-11/11 - 01/17 9 3 2 3 1 2 9 3 -io 1 9 - = 1[ A B + x+2 x-1 + C…

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Q: 3 (5æ° + 2x") dx - 4 Find

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Q: Evaluate the integral (4x -7/13 – 5x13)dx. „7/13 (4x -7/13 - 5x13)dx help (formulas) -

A: We first distribute the integration

Q: (1) 2x₁ + 3x₂ = 8 x₁ +4x₂ = 9 (Ans. x₁=1, x₂ =2)

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Q: Find the value(s) of z which satisfies the equation |z|2 + 1 + 6i = 6z.

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Q: 18. 8x So (42.8210) dx A) undefined B) In(6) – In(10) C) In(10) - In(6) D) ln(6) – In(10) + C E)…

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Q: 3.2 X(x²-1)-y=xy* ;y(2)=-

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Q: (VI 1 1+t-4 6 tv1+t / 1 t/1+t-4

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Q: 8 dx sec 2x-1

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Q: (cscd + Co+0)(1-CosO

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Q: If A = 2 1 2. show that A² – 4A – 5) = 0, %3D %3D 12 2 1.

A: To show that  A^2-4A-5I=0

Q: - 1 Find ²¹ dz x² +C

A: As we know that, The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And use…

Q: Find x. 1.

A: As you have posted multiple question in this question so I have solved first three parts as per our…

Q: .2 -dædy In (x) ey

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Q: 4) We know that () and a!=1.2...a. Prove that Yn75, )< 2n-2. G0od Luck!

A: Given, ab=a!(a-b)!b! and a!=1.2....a

Q: S Sech (ax-

A: Evaluating the integral of hyperbolic function using substitution.

Q: If y = ((5z² + 8z)³ – 5-)°, then dy/dr is:

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Q: Problem. Show that S {₁ 【 (s − 2)(s − 3)(s — 6) J L-1 -6)} = 1/2 ²² - e³t + e

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Q: Let v= (4,1). Carry out the following computation. Find -7v. |- 7v| = D %3D

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Q: 7.2.17 Show that To Ta dx (x² + a²)² = Л 4a³' a> 0.

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Q: 5. Find dy dx of √xy + 2x = √√√y

A: Topic = Derivative

Q: 4 4 + x2 Find 3 x° + + 4/x ) dx - -

A: Given integral, ∫x3+4x+4x2+4xdx

Q: afdæ dx Find + C

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Q: and /( 2²/7 + 2x + 4) dx 3 X2

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Q: 1.1 Find the value(s) of z which satisfies the equation |2|2 + 1+ 6i = 6z. %3D

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Q: Find d. dr /1 + x²

A: We have to find the derivative and then anti derivative.

Q: Show that 1 1 2 y? 2 = (y? – *)(2² – a²)(2² – y') 4,

A: We have to prove that  We will it by using the properties of determinants.