Cn = COS * ´π(1+4n)` 2

Q: Vectors [2, 5, a] and [-6, b, 9] are collinear. What is the value of ? a a) 5 b) -3 Oc) -5 d) 3

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Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

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Q: Determine an equation for normal to the curve y = at x = x = -2.

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Find the average value of the function f over the interval [0, 15]. 4 f(x) = x + 1

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Q: S I (s - 2)² Option 4 Option 3 ★ Find laplace transform for -| (s-3)2 Option 1 O Option 2 O

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Q: Evaluate the integral: 18x² √64 x² - I dx

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Q: 1. Find the first 3 terms in the Maclaurin series for the function f(x) = sin2x 2. Find the first 3…

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Q: In r Т lim, 0+ 01 O II O III OIV O Not Indeterminate

A: Hee, the given expression is: limx→0+ln xx

Q: 31. The function fƒ: R→ R is defined by f(x) = (a) Show that f is a bijection. (b) Determine f¹(x) x…

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Q: If X(z) is the z-transform of the signal x(n), then what is the z- ?transform of the signal x(-n) x…

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Q: APPLICATION OF 1st ORDER DIFFERENTIAL EQUATIONS 1. Brine containing 3 lb/gal of salt enters a large…

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Q: Convert the following iterated integrals (SET UP ONLY): x² a.) [f dA from Cartesian coordinates to…

A: The simple change polar coordinate...

Q: 12. etan 2x sec² 2x dx 13. Jdx/(x²-4) 14. (2x¹-x²) dx / (2x² + 1) 15. f (sec²x) dx/(√(1-4 tan² x))…

A: Given

Q: t b) tz 16) L-¹ (5-3)²+25) = c) tz estsinst a) 5 d) t est sin3t 5 b) c) e-at sin3t 5 eatsinst d)

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin (3t), y (0)…

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Q: Find example where of is continuous and an - bijective but f¹ is not

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Q: 13. dx/(x²-4)

A: Since you have posted multiple problems we will answer first problem for you. If you need any other…

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: If you apply the direct comparison test to assess convergence of 1 - to which of these series would…

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Q: *2t-h 5 if t=2 then h = -1 true O false O

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: We have to use the Euler method

Q: Question 4 (a) Solve the following: 4x¹dx (b) Explain with the aid of a sketch how this value can be…

A: we have to find the value of integral ∫-22 4x4  dx

Q: Find the integration of the following functions COSX 1) dx 3+8sinx 2) fx tan(x² + 1)dx

A: In this question, we want to solve the given integrals.

Q: let A be a bounded. Sup A non. n-empty set in R show that is a limit point of A.

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Q: (2x-1)dx 2x³-x²-27x + 30

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Q: Solve the following Differential Equations with Laplace Transforms y" - by' + 15y = 2 sin (3t), y…

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Q: Determine dx for each of the following functions. Do not simplify the dy expressions after applying…

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Q: How firel the center, foci, vertices and eccentricity for the following equations! x+4y²-4x-8y +4=0…

A: Concept: Ellipse: The equation of the ellipse with center at (h,k)  (x-h)2a2+ (y-k)2b2 =1 Hyperbola:…

Q: Q3/ Solve dy dx4 2d²y + 1 = 0 dx²

A: Given d4ydx4-2d2ydx2+1=0To find solution:

Q: √4x²(x³-5)ª dx = Ox³(x¹² - 25x¹ +250x6 - 1250x³ +6250) + c 12 15 O 16(x³ - 5)4 + c ○(x³ - 5)5 + c…

A: To evaluate ∫4x2x3-54dx Formulae used d(xn)=nxn-1d(constant)=0∫xndx=xn+1n+1+c

Q: P3: Calculate the volume of solid of revolution when the region bounded by y = cos x and x² - y - 2…

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Q: Q3) Given, u (x, y) = xy is harmonic, find a harmonic conjugate v(x, y), write u+iv as a function of…

A: As we know that for complex analysis z=u+iv   then u and v are conjugate to each other.Then by…

Q: State, with explanation, the truth value of the following statements. x²-x-2 a) x = 2 is a vertical…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: * The following matrix is a 100 020 0 004 identity matrix O skew symmetric matrix O none of these O…

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Q: 1. Consider the function y = ex²-3x+1. Find the extreme value of the function (classify as minimum…

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Q: 3. A farmer has 6000 m of fencing and wishes to create a rectangular field subdivided into four…

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Q: 20. Stan² x dx

A: Consider the integral  ∫tan2x dx

Q: Find the volume of the region of R^3 bounded by the paraboloid z=x^2+y^2 and by the planes…

A: Concept: Let us take D to be a bounded, closed space region. Let a and b represent real numbers,…

Q: 3 M8 n=1 (Inn) 13/2

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Q: Find the Jacobian for z = ² + 8uv and y = 6uv². Jacobian (equation format)

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Q: If [ f(x) dx = 12. g(x) dx = -2 and L₁ dr following gives the value of [[1²)+ 4 76 Sh +4g(x)- h(x)…

A: Given:     ∫-36fxdx=12     ∫-36gxdx=-2     ∫-36hxdx=-7

Q: C. Evaluads the Sum 20 [ (₁²+3) ² (

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Q: 1+1=

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Q: k 1. Find the value of in a. 0.298597 C. 0.498597 2. Find the value of a. 0.138629 c. 0.158629 k in…

A: Solution

Q: Find the arc length of the curve on the given interval x (0) = 0³, y (0) = 0² ; 0 ≤ 0 ≤ 2

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Q: X5 x3 +4 +4 dx

A: WE can find the integration as below.

Q: expand using the binomial theorem. simplify (a+b)^2 (2x^2 -1/x^2)^4

A: solution

Q: Q1) L-1 s(s²-1) = a) cosht-1 Q2) The general solution of y"" + 2y"-y' - 2y = 0, is: a) y(x) = c₁e²x…

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