Evaluate cos √6x dx using a substitution followed by integration by parts.

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A: To solve the higher order differential equation.

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Q: 4a) S 3x+7 (8+6x-9x²) 3/2 -dx 4b) S 2x²-11x-1 (x+3)(x² +1) -dx

A: ∫un du =un+1n+1+C ∫sec2(u) du = tan(u) +C Note : As per our guidelines ,we can solve first question.…

Q: stion T1_Q3 rove by contradiction that there are no positive integers p and q such that 4p²-q² = 25

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Q: Given that f(-10) = -0.1 and f(-9.6) = 1.8, approximate f'(-10). f'(-10)

A: We know, f'(x)=f(x+∆x)-f(∆x)∆x Let, x=-10 and ∆x=0.4

Q: Q3/ solve the differential equation below: 1. ²-3x+2y=0 (Complementary Function)

A: topic- differential equations

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Q: 4. · [ (8x − 3) (4x² – 3x) ³ da x J dx - 4x² x S dx 3 - 5x² 5. 6.

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

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A: Solve the following

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A: Use minimizing concept

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A: A detailed solution is given below.

Q: PART I. Calculating First Order Partial Derivatives 1. f(x, y) = 2x² - 3y - 4 3. f(x, y) = (x² -…

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Q: Find the derivative of the function. <-2 g(x) = (7x² - - ² 4 4x + 7 g'(x) = 2 ((7x²-4) (28x²…

A: g(x)=7x2-44x+7-2 Chain rule: f(u(x))=f'(u(x))·u'(x)

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A: answer is in next step

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Q: Find the nth Maclaurin polynomial for the function. f(x) = ex, n=5

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Q: (a) If (tanh x) = 1/4, find the value of sinh x without a calculator. Show the procedure of your…

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Q: All exponential functions can be written in many forms. Write the function -0.08t f(t) = 340e- in…

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Q: Solve for the homogeneous linear equation given below 1. xydy- (x + 2y)² dy = 0 O-In ()-4lny = C…

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Q: Let R be & (t) = a vector based function defined loy < 1/2, 1, 0) if t = 1 3-√E 1-t² It cos nt if…

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Q: Find the absolute extrema of f on the given closed interval. 1. f(x)= x³ + 3x² - 9x ; [-4,4]

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Q: 3 Jess bought a new car for £12 000. In the first year the value of the car depreciates by 20%. In…

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Q: Find derivative of the following function. 7x -7x + e y = X

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Q: Q2: dy du (A) Show that if y=csc(u), then -csc(u) cot(u) dx dx

A: SOLUTION-

Q: 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

A: Given a=i+2j-3k b=2i-j+4k Aim : to find unit vector perpendicular to a and b

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Q: 5. r(x, y) = ln (x + y)

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Q: Suppose A = 4i-6j, B = i + 7j, and C = 9i - 5j. Then the scalars h and k such that A = hB+ kC are…

A: Topic = Vector

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A: As per bartleby guidelines we only give first question answers.

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Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

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A: Concept: linear equation in three variable solutions: a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3…

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Q: Prove that √1+i√3+√1-i√3 = √6

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A: Given,  f(x)=x

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Q: dy dr = cos(²) +

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Q: 7. A 25 kg mass is suspended from a ceiling by two cords. The cords make angles of 45° and 70° with…

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