Evaluate: [8zº · sec² (25) dx =

Q: The cost for producing a thousand widgets is given by C(x) = 0.06x4 - 2x³ + 14x² + 400x, 0 ≤ x ≤ 60.…

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Q: The graph of f(w) = 9 is given below. 10- 8 6 5 4 -4-3 -2 -1 3 1 2 3 4 5 6 7 8 9 Determine the…

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Q: antiderivative. Use C for the constant of integration. 1 3 cos² (4x) F(x) = (In(|sec (4x) +…

A: Given The aim is to find the antiderivative of .

Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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

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Q: them by mteger values. For each of the following logarithmic expressions, give the two integers that…

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Q: (11,20) (11,20) Show that (40) fdx+ gdy = f(4,1) 24x²y³dx + 40y^³dy is independent of path: J(4,10)…

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Q: Evaluate the following improper integral. So e 0 e-bt sin (at)dt, where b=2, a=1 Round your answer…

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Q: Find the integral. Use C for the constant of integration. | (x² (y² + 3)² dy

A: The objective of the question is to find the integral of the given function with respect to y. The…

Q: А = 1 1 1 3 4 -3 - 1 0 2 B || 8 -2 1 -3 1 0 - 4 1 1

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Q: The curve r(t)= (f(t),g(t)), where f and g are twice differentiable, has f'g'"-f"'g' curvature…

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Q: Find the cost function for the marginal cost function. 7 C'(x)=9x; 10 units cost $171.99 X Write the…

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Q: how that the function is increasing on the given open interval. (Enter your answers as a…

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Q: Find the volume of the solid generated when the shaded area is revolved about y = -1. y y = 2x y=x²…

A: To find the volume of the solid generated when the shaded area is revolved about .

Q: For what value of a is the following function continuous at every x? f(x) = x²-30, x<10 x≥ 10 ax,…

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Q: I For f(x) = x-2 4x+20 (a) f(-6) (6) f(2) (C) f(-5) (a) f(a+3) find

A: The given function is To find:-

Q: Find the volume of the region under the surface z=xy^2 and above the area bounded by x=y^2 and x+y=2

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Q: Let g(2) = 42³ +7z7 Determine the most general indefinite integral of g. | (42³ + 7z") dz =

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Q: Solve the following Initial Value Problem. dy dt - y= sec² (t) + 3 sin(t), y() = 1

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Q: Solve the matrix equation for the unknown matrix X, or explain why no solution exists 19. 1/5(X+D)=…

A: (1/5)(X+D)=C Multiplying both sides by 5, (X+D)=5CSubtracting matrix D from both sides, X+D-D =5C -D…

Q: Find the integral. Use C for the constant of integration. | cv² (y² + 3)² dy

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Q: A biologist has two brine solutions, one containing 2% salt and another containing 8% salt. How many…

A: The objective of this question is to find out the amount of each brine solution needed to create a…

Q: 9. In the following exercise: i. Identify the function's local extreme values in the given domain,…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, Kindly…

Q: Let f(x) = x if x ≥ 5 5 if x < 5 a. Find f(1), f(5), and f(7). b. Sketch the graph of y = f(x).

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Q: 1 •[₁ F(X) -1 Given f(x) dx = 0 and (a) [f f(x) and [₁ f(x) dx. 1 (c) [₁² (d) (b) • [² f(x) dx - [°…

A: (a)

Q: If f(x)= g(x)/ x, and g(x)= x + cosx  (defined at interval 0, 2π) Find the slope of the tangent…

A: Given that the expression f(x)= g(x)/ x, and g(x)= x + cosx  (defined at interval 0, 2π) we have to…

Q: Find the difference quotient of f; that is, find f(x) = 3x² - 4x + 4 f(x+h)-f(x) h h#0, for the…

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Q: 5. Using Geogebra, draw the polar curve, r = sin³ (2.50) +cos³(2.50),0 ≤ 0 ≤ 2ñ.

A: Consider the curve

Q: 2 sin(x) cos(x) + √3 sin(x) = 0 Find all angles in radians that satisfy the equation. For each…

A: The given equation is;2sinxcosx + sqrt(3)sinx=0

Q: Let h(z) = 2¹/3 Determine the most general indefinite integral of h. 1/3 dz

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Q: The domain of f(x, y) is the xy-plane, and values of f are given in the table below. Find fe grad…

A: To find the line integral of a scalar field f(x,y) over a curve C, the general formula is:Segra…

Q: he letters x and y represent rectangular coordinates. Write the given equation using polar…

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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: logarithms. Express powers as factors. 1. A 50-mg sample of a radioactive substance decays to 34 mg…

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Q: Convert the Cartesian coordinate (-2,-5) to polar coordinates, 0 ≤ 0 < 2π r = Enter exact value. 0 =

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Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

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

Q: The graph of a one-to-one function f is given. Draw the graph of the inverse function f¹. For…

A: The graph of a​ one-to-one function  is given. To draw the graphof the inverse function .

Q: Evaluate the following limits algebraically. 2. lim x---> 2^-      (x+4) / (x^2 + 2x - 8) 4. lim…

A: To evaluate the following limits.

Q: f(x)=x^[8/3]-4x^[2/3] determin the: a) roots b) Domain c) intervals for which the function is…

A: The given function is To find:-rootsdomian intervals for which the function is positive and negative…

Q: 2. Σ. 1 (-5) 2n n2gn

A: The given series is The Root test If L&lt;1 then series is absolutely convergent If L&gt;1 then…

Q: Evaluate 7x 11 √(x - - − 1)(x – 3) - - - dx

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Q: Determine whether the function shown below is a one-to-one function. If it is one-to-one, find its…

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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: please i dont understand that you did after step 3 from 0=sin(2pi c)

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Q: 2x - 5y = 7 3x + 2y = 4

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Q: A tall pipe is 30 feet tall. A person with a height of 6 feet walks away from the pipe along a…

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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 the equation for the line tangent to the parametric curve: at the points where t = 4 and t =…

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Q: When solving the auxiliary equation associated with the differential equation 3y"+2y"=0 it is…

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Q: Question Find the area A of the region that is bounded between the curve f(x) = -2 sin () - 3 and…

A: To find the area A of the region that is bounded between the curve  over the interval .