8. The position function of an object is defined as: s(t)= t³-t²- 8t Find the minimum velocity of the object.

Q: 59-62 Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d evi dt sin sin…

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Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: 3. Suppose that the revenue in selling a tables is equal to 200x -0.25x² dollars, and producing a…

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Q: 19. TT/2 -π/2 sin 0 de 20. * sec² 0 de

A: 19 ∫-π/2π/2 sinθdθ [-cosθ ]-π/2π/2 0 - 0 =0 other way sin is odd function so also integration is = 0…

Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: 1) fx-²dx 2) sin(n)dx

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Q: 62. du * |x|dx

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Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: 2. y = tan-¹(cosh x) (sin² x) (sech x) secx [use logarithmic differentiation]

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Q: Find the Maclaurin series centered at c and the interval of convergence. 12) f(x) = 1-2x 13)f(x) =…

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Q: Find the point of intersection (xo, Yo, Zo) of the lines given as: o = i i i Vo = Zo = L₁: x= 7+t, y…

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Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

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Q: dy/dx of sec^2 (x^pi - pi^y)

A: To find the derivative of given function.

Q: /² sin ( cos() sin() dx (Consider initially the first 2 terms)

A: To evaluate the value of given integral.

Q: Given: : Saxasin(2x)dx = - ㅠ (A) 3 Зп B 4 c D E 2 3 4 277²-24 64 5T Find bif sbst

A: Let's find.

Q: The conic section whose equation is x2 - 3y2 - 8x + 12y + 16 = 0, is ______. centered on the origin…

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Q: ://v². dx √1-x² dx √√2. x√x²-1 (ª (¹² - 31/₁) dr (1. 25. 27. 29.

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 4x+14 between x =…

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Q: IV. Find Do not simplify your answers. dy dx 1 1. cos x + y² = x coshy - 2y, where x > 0

A: Given problem:-

Q: 19 Give the properties for the equation 9x 2 + 16y 2 - 36x + 96y + 36 = 0 Major Axis 8 16 9

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Q: Integrating Factor by Inspection: 7. xdx + ydd = (x² + y²)dx

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Q: Find the laplace transform of ƒ (t) = 3t³ − 2e²t + 2 cos 2t OF (S) = OF (s) = OF (s) = OF (s) = OF…

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Q: Compute the area bounded by the curve x=y²-2y and the line x-y-4-0₁

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Q: Consider the partial differential equation u, + uux = 7+ uxx: Determine the order of this equation;…

A: Given differential equation:- ut +uux =7+uxx

Q: Find the slope of the normal line to the graph of g(x) = = at the point where x = 0. sin¯¹(x)+e²

A: Slope of the Normal line to the curve f(x) is -1f'(x).

Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Find the vector component of v = 2i - j + 3k along b = 4i + 8j + 8k and the vector component of v…

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Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why. a- Lim 4 c- lim…

A: See the details solution in below

Q: [₁x³√x² + 3dx x-3 2

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Q: Show that the differential equation xºy7 + x(1+yº)y' = 0 is not exact, but becomes exact when…

A: Take the partial derivative of coefficient of dx and dy to show that the given differential equation…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

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Q: Find the arc length of the graph of r(t) = ev NOTE: Enter the exact answer. L = 451 e√²ti + e-√² +…

A: Here we have to find the arc length of the graph of r(t)=e√2ti+e-√2tj+2tk , 0<=t<=√2ln5.

Q: Solve the given differential equation. All solutions should be found. dy 2xy + y² + 7 dx x² + 2xy…

A: To find the solution of given differential equation in implicit form.

Q: Find the directional derivative of f(x, y) = direction of Q(2,-2). NOTE: Enter the exact answer. √2…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. 10 ||ti + Pi|| dt = t²i||dt 1014.07 3…

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Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

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Q: d an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (4,…

A: Given; Points- (0,0,0),(4,0,6),(-4,-1,8)

Q: of

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Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

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Q: Evaluate 7664/7 [²² (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

A: We have to evaluate of given integral

Q: B f(x)da as positive, negative or zero? Note two vertical lines indicate a Is Area = and B. Select a…

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Q: f(x,y) = 3x-2y. R÷ the circle x² + y² = 1

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Q: (x + 2)(6x - 1) (6 - x)(4x + 2) Find the horizontal asymptote of f(x) = 4- y=

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Q: dw a) Find for the following function. dt w = 2ye* -In(z), x = ln(t2 + 1), y = cos(2t + 2), z = et…

A: If w=f(x,y,z) and x =g(t),y=h(t) , z=u(t) then,    dwdt =∂w∂x.dxdt+∂w∂y.dydt+∂w∂z.dzdt. Note : As…

Q: 3. x dy + 6y = 3xyi dx

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Q: (C) EXERCISES Evaluate the following integrals: 1. tan² x dx 2. cot cot² r dr COS I da sin x COST…

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Q: Integrating Factor by Linear Equations: dy 11.42 dx =

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate the integral √(4 by making the appropriate substitution: u √ (432² dx [ X (4x² + 11) 7 = X…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

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