Find the indefinite integral. x¹ + 24 dx = +C

Q: Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = -1, v(0) = -7,…

A: Given that u and v are function of x that are differentiable at x=0At  To find:we have to find the…

Q: f(x) = -3x + 5 g(x) = x² = x² + 2x + 15

A: Given the function   we have to find the value of (gof)(x)

Q: Solve the rational inequality x²-9 x² - 49 -≤0.

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Q: Find the indicated term of the binomial expansion. 13 (u³ +21²) ¹³₂ ; tenth term

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Q: (– ²/6) has exactly one point of inflection with a positive x-coordinate. What is the x-coordinate…

A: The given function is .The aim is to find the point of inflection.Definition:If  is an inflection…

Q: Find the unit tangent vector T and the curvature x for the following parameterized curve. r(t) =…

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Q: If you know that Q(x) is a quadratic function and that Q(5) = 10, Q(8) = 11 and Q(1) = 9 then: 1…

A: If you know that  is a quadratic function and that , then to evaluate the following integral.

Q: Find the radius of convergence and interval of convergence of the series. Σn!(3x−1)″ n=1

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Q: Let g(z) = √√23 Determine the most general antiderivative of 9. | √dz = [

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Q: x+6 (x + 2)2 dx

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Q: Find the indicated term of the binomial expansion. 10 (m-n) ¹0 ; fifth term

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Q: Find the volume of the solid obtained by rotating the region bounded by the x-axis, the y-axis, the…

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Q: Evaluate the surface integral      SF · dS  for the given vector field F and the oriented surface…

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given,

Q: 8. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval [0, π/2], are…

A: The given functions are the inner product of two functions f and g on the interval [a, b] is the…

Q: Convert the rectangular coordinates of the point to polar coordinates (r,0) with r>0 and 0 ≤0<2.…

A: We need to convert rectangular corrdinates to polar coordinates.

Q: 8. p-series below: (a) n=1 Use this fact to find the sum of each series below. (You may express your…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: The answer is wrong

A: The given curves equation is

Q: At what points is the function y = X+5 - 8x + 15 x²- continuous? Describe the set of x-values where…

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Q: Find a power series representation for the function. f(y)=In f(x)= In[11+y)

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Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population…

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Q: Consider the following function. T 3 π f(x)=sinx, a ==, n=4, 0≤x≤: 6 a) Approximate f(x) by a Taylor…

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Q: 3 fff Sayz dv= - S₁² S₁² ² 8zyz dz dz dy 2

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Q: Find the centre of mass of the region between y = x x² and y = x³ from x = 0 to X = 1.

A: The objective of this question is to find the centre of mass of the region between the curves y =…

Q: For timer 20, the function Cate with positive constants a and b gives the concentration, C, of a…

A: The given function is

Q: Given y = f(u) and u = g(x), find - (3) ² y=9u-5, u= dy dx = f'(g(x))g'(x).

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Q: Make a sketch of the region and its bounding curves. Find the area of the region. The region inside…

A: I have appended the formula used in the solution procedure

Q: Find the unit tangent vector to the curve at the specified value of the paramet r(t) = t³i + 3t²j, t…

A: The given equation of curve

Q: Let f(x) be a continuous function for which we know f(2)=3, f(4) = 5, f'(2) = 7, and f'(4) = 19.…

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Q: Find the time of flight, range, and maximum height of the following two-dimensional trajectory,…

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Q: Evaluate the given definite integral. 3 [(-8 -4 (-8z - 7)dz =

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Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: The objective of this question is to find the critical numbers and the open intervals on which the…

Q: Given the parametric equations Compute the derivative dy/dx as a function of t. -t³, y = 6-3t x =…

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Q: A= B n ed Use the right triangle and the given information to solve the triangle. a=1, c= 8; find b,…

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Q: The system of differential equations : has the solution Y = C₁ et V₁ + C₂ ezt V₂ + C3 e¹³ V3 where…

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Q: Find a power series representation for the function. ( ) = n( 11 + y )

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Q: Evaluate ∫∫∫E 1/(x^2+y^2+z^2 )dV where E lines between the spheres x^2+y^2+z^2=4 and x^2+y^2+z^2=16…

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Q: Evaluate the limit, use L'Hospital's Rule when possible. limx→0 5x In(x+2) O-5 01/2 0 5 Not Possible

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Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

A: from the given table

Q: Sketch the graph of the quadratic function. f(x) = x² — 20x – 800 - -

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Q: Consider the triangle below. Click on the picture to see it more clearly. If c = 4, the angle C =…

A: Given,

Q: Suppose that the variables x and y are related by the implicit equation X V = -3.3x 1.8 ln(x)+2.8y—…

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Q: The system of first order differential equations y₁ = 5y₁ + 1y2 y₂ = −4y₁ + 1y2 where y₁ (0)= 4, y2…

A: The objective of the question is to verify if the given functions y1(t) = (4 - t)e^(3t) and y2(t) =…

Q: The figure below shows the derivative F'. If F (0) = 15, give (x, y)-coordinates of all local maxima…

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Q: r = sin(20), r = cos(20)

A: Given that the polar curve

Q: Consider the following. f(x) = -3x² + 36x Find the critical numbers. (Enter your answers as a…

A: The objective of this question is to find the critical numbers of the function f(x) = -3x^2 + 36x…

Q: If f(x) - Sto = t5 dt then f'(x) = and ƒ'(−4) =

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Q: Your company determines that the marginal cost, C', of producing the xth unit is given by the…

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Q: The position of an object in circular motion is modeled by the parametric equations x = 9 sin(2t) y…

A: Note: Due to guidelines, I can solve only first 3 sub parts.

Q: Find the center, foci, and vertices of the ellipse. Graph the equation. 4(x + 5)2 +8(y-2)² = 32 Find…

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