If f'(x) = 2x³ + 3x² − 4x + 5 and f(0) = 1 and f'(0) = 2 find f.

Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: The function f(x) 2x³ + 42x² = one local minimum and one local maximum. This function has a local…

A: You must have an idea how to use derivatives to find the local maximum and minimum using critical…

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Q: Find the area common to the circle r = 3 and the cardioid r = = 3(1 - cos 0)

A: Figure of area enclosed by both curve÷

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A: You need to find out the critical points then solve for maxima & minima. The explanation part is…

Q: Consider h(x, y, z) = ln (xy) —sin (y²)+e** at the point P (1,1,0). 1 the following: (a) the…

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Q: Determine the slope of the tangent line to the curve of sin(x + y) = y2cos(x)  at  the point (x,y) =…

A: Topic = Derivative

Q: cos e de sin² 0 + 4 sin 0-5

A: To evaluate the given integral.∫cos θ dθsin2 θ+4 sin θ-5

Q: Its tot as TR = 300q - 6q² and its total costs as TC = 4q². a) Determine the optimal quantity and…

A: Given

Q: Question 4 (a) Solve the following: √4x² dx (b) Explain with the aid of a sketch how this value can…

A: Let's solve given integral.

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Q: 2. Find d using implicit differentiation. Enclose final answers. dx (a) √x=y=√√√x + y = 5 (b) xsin y…

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Q: ל 15 18 a = (3₂16) 6= (-2,0,1) → 08 -> 2² = ²²-23 +5k →> oc CẢ OA

A: Given :a→=3,1,6=OA→b→=-2,0,1=OB→c→=i-2j+5k=1,-2,5=OC→

Q: Find the maximum and minimum value of the function and the inflection point of the given curve…

A: Given :

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Q: z, 1 + 9 + 25 + 49 +81 + ... + /2/

A: Topic = Algebra

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Q: 2 S-2 2 S+2 Option 3 Option 2 O *The Laplace transform of the x(t) is 2e21 1 S - 1 s²+1 Option 1 O…

A: Let's do laplace transform of given function.

Q: integral

A: We will find the solution m

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: Q1) L-1 a) cosht -1 b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of y"" + 2y"…

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

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Q: lim,+1+(1²-2-²-1) In

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Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

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

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

A: Let's solve diffrential equation by using laplace transform.

Q: 17. 18. 19. dx/ (9x² + 4) sin³ x cos x dx (secs x) dx / csc x

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Q: Obtain the an = $ sum of the series. (sin-—-sinn) W

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Q: Which of the following functions is entire? For each, justify. f(z) = (x² - y²) - 2xyi

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Q: 5.494949... = 5. 49494 100000 X

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Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

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

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Q: Find the normal line to f(x) = ax² - 4ax at x = 3. Assume that a is a positive constant. Next…

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Q: uestion 4 (a) Solve the following: 4x*dx (b) Explain with the aid of a sketch how this value can be…

A: A detailed solution is given below.

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: A = 1 4 2 4 व B = [2 00 Tonm 0 4 -2 1 D = -2 0 0 0 1000 0120 0 1 1 1 1

A: Concept: Determinants: For a square matrix, a determinant can be defined in several ways. The first…

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Q: Question 5 limx→→+∞ (1 + ¹)² O ll SO III OIV O Not Indeterminate

A: Please mention also what the first four options wants to represent here ...as correct answer is e .

Q: Instructions 1. Write your complete solution for each item. It should be handwritten. 2. Make sure…

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Q: Question 4 (a) Solve the following: [²4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: 6 sinh t 6 cosh 51 Option 2 O Option 3 * What is inverse Laplace for 6s s² +25 6 sint 6 cos 5t…

A: In this question, we need to find the inverse Laplace of given function.

Q: Prove that the following functions u/v are harmonic; then find the conjugate harmonic function v/ u.…

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: Show that any subset of bounded set is bounded

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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: 4. A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

A: where r= radius and h= heightVolume of a right circular cylinder cylinder is πr2h. Volume of a…

Q: 1. dx/(x - 1)³ 2. (1-x²)² dx 3. f (x² - 1) x dx

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Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A: We have to prove the given equation of complex number