Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each integral, you must write down the relevant integral rule and show your work in evaluating the integral. Give your answers as fractions or in terms of a. 3 (i) dz

Q: Find the maximum value of the function f(x) =x² - 9x2 + 15x-5. Answer

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Q: ind cylindrical coordinates of the point with rectangular coordinates (3, –3, –7).

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Q: Find an equation of the plane with the given characteristics. The plane contains the y-axis and…

A: Plane in 3D: The equation of a plane in 3D is ax+by+cz=d If by is removed, the graph of the…

Q: onsider the following planes. -4x + y + z = 4 12x – 3y + 4z = 16 a) Find the angle between the two…

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Q: Consider the function  f(x)=4/x^2−3/x^5. Let F(x) be the antiderivative of f(x) with F(1)=0. Then…

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Q: Direction: Find the differential equation of the family of curves described. 4. Ellipse with center…

A: Equation of ellipse is x^2/a^2 + y^2/b^2 = 1

Q: The region bounded by the given curves is rotated about the Specified cukis. Sketch the region and…

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Q: vo Variables 4)dr + (2r. (2. 4x)dı

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Q: Select from multiple choice and fill in the blanks

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Q: Several statements about a differentiable, invertible function f(r) and its inverse f-(z) are…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Let the region R be the area enclosed the function f (x) = x2 + 1, the horizontal line y = 6, and…

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Q: y dy J 725 – 16y 2.

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Q: Which of the following is NOT a solution to the trigonometric equation 2 cot 0 cos 0 – cot 0 = 0? 2…

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Q: Differentiate. f(x) = e 13x f'(x) = |

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Q: (b) If a > b and c > 0, then ac > bc.

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Q: Find Ay and f'(x)Ax for y = f(x) = 6x°, x = 4, and Ax = 0.06. Ay = (Round to four decimal places as…

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Q: 7y" - 18y %D

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Q: 1. cot? 2x csc* 2x dx

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Q: y = 5x – 6 tan x, concave upward concave downward

A: Given problem:- y=5x-6tan(x) , (-π/2, π/2)  Determine the open intervals on which the graph is…

Q: f(x + Ax) - f(x) Find lim Ax-0 Ax f(x) = 3x- 9x %3D Step 1 Find f(x + Ax) by substituting x + Ax in…

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Q: A rectangular lot having an area of 5000 sq meters is to be fenced on three sides Find the minimum…

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Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

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Q: If f(x) = e*sinh x, what is f'(x)? e*(cosh x- sinh x) O Option 1 Option 2 e*(sinh x - cosh x) 2e2x…

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Q: Direction: Solve the following equations using separation of variables. 3. 2xy + 6x(x² – 4)y' = 0…

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Q: Pharmaceutical theft has been rising rapidly in recent years. Experts believe that pharmaceuticals…

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Q: Using any methods discussed, find atleast 1 root for each problem. Upload your solution at the space…

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Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: Solve the system of linear equations using Gauss-Jordan Elimination and Reduced Row Echelon Form…

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Q: statements is NOT true?" a = 230, b = 150, C = 95° The length of the third side is 25.13 unite The…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Evaluate ſV7– x²dx

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Q: r(3x² x + 8x – 12)d: .3 x' +7x +12x

A: Given:          ∫3x2+8x-12x3+7x2+12xdx Factor the denominator:       =∫3x2+8x-12xx+3x+4dx The form…

Q: 1. The Fibonacci sequence is given by the recurrence relation a, = a,-1 + a,-2; a, = 0, a, =1. Write…

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Q: What is the value of the trigonometric expression below? * sin 0° + sin 1° + sin 2º + sin 3º + ... +…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

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Q: Determine whether each point lies on the line. x = -2 + t, y = 4t, z = 5 + t (a) (0, 8, 7) O Yes No…

A: topic - lines and points

Q: Find dy. y = vx + 10 dy = (Simplify your answer.)

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Q: What is the edge of a cube whose volume is equal to that of a rectangular bar measuring 100 cmlong,…

A: Let the edge length of the cube be 'a' units

Q: A mass that weighs 8 lb stretches a spring 48 in. The system is acted on by an external force of 8…

A: Given

Q: Solve the initial value problem. d?r 2 dr = 5, r(1) = 4 dt2 dt t=3

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Q: Find the orthogonal trajectories of the given family of curves. Draw a few representative curves of…

A: For orthogonal trajectory we replace dy/dy by -dx/dy

Q: Bernoulli Equation (10) y'+3x²y = 4x²y² (11) (x²y* – 1)dx + x³y³dy = 0 (12) x2 4y + 2xy = 5y3

A: Note : As per our Guidelines , we can solve first question . Please repost remaining question.…

Q: Write an equivalent exponential equation. 2 log 8 4= 2 /3

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Q: The length of a rectangle is two-fifths of the radius of a circle. The radius of the circle is equal…

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Q: what is the minimum value of f(x)=3x2-18x+25 a. -2 b. 3 c. 6 d. -18

A: Given  f(x)=3x2-18x+25

Q: (3 - 2 3 – 4cos dx

A: The given integration,     ∫3-4cosxπ2 dx

Q: Find the maxim um and minimu m value s of the the constraint x2 + y? + z? = 400. Maximum value is…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: 12 dx Evaluate the integral: (9+3x)3 63 1. 36 1. 99 None of these 72

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Q: 'ind the exact length of the curve x = t sint y = t cos t or 0<t< 1. ou may use the following result…

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