Evaluate: S(4sin (x) – 3sec? (x)) dx

Q: A cup of hot coffee is placed in a cold room. The temperature (in degrees Fahrenheit) of the coffee…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 r(t) = e"i+ etj %3D K(t) = ||

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Q: Evaluate: da Væ2+4

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Find an equation of the plane. The plane through the points (2, –1, 3), (5, 3, 6), and (-3, -3, -3)

A: We are asked to find the equation of the plane

Q: In Exercises 1-4, solve the given initial-value problem. (For Exercise 3, you may "complexify" the…

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Q: Fill in the Venn Diagram below by dragging the appropriate entry to the orrect location given that:…

A: Explanation of the answer is as follows

Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t< v2 In 5 NOTE: Enter the exact…

A: Let's find.

Q: Find the net signed area between the graph of the function f(r) = -x-4 and the x-axis over the…

A: To find the area between the line and x axis.

Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

A: Let x be the acute angle made by the telescope with the vertical.

Q: What is the absolute maximum value of f(z) = z³ – 3z² +4 on the interval (-1, 1]? %3D (A) 4 -2 (C) 0…

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Q: Find f"(0) for the function f(x) = (x+1)e².

A: Given query is to find the Indicated derivative

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the arc length L of the graph of r(t). r(t)= 4 cos(t)i + 4 sin(t)j + tk, 0 ≤ t ≤ 2π

A: The formula for the arc length is given by: L=∫02π(x'(t))2+(y'(t))2dt Here,…

Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

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Q: Write the equation in standard form. (Use xp for x’ and yp for y’

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Q: dx メ-1

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t*|dt (25;² + 1) – 1 3j2

A: The given integral,                        ∫05ti+t2jdt

Q: | (2x - y) dx + (x + 9y) dy. Ic Evaluate C: x-axis from (0, 0) to (0, -9) and (0, -9) to (5, -9)

A: We can solve as follows

Q: actorise the polynomial 2x3 – 3ix² + 2x – 3i. Show all working.

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Q: Formulate a linear programming problem that can be used to solve the following question. An airline…

A: We need to give constraint equation.

Q: dx 1-x2

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Q: re

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Q: The SMPT group at UB sells past final exams packages (small and large) for $2 and $3 respectively.…

A: topic - linear equations

Q: am dA y² dx + x² dy = / / ( - əx ду for the given path. hC: rectangle with vertices (0, 0), (2, 0),…

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Q: Compute the composite functions fog and gof and discuss their domains, where f (x) =vx, g(x) = 1 –…

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Q: An object with an initial position of x(0) = 5 has a velocity of v(t) = sin 2t. %3D %3D What is its…

A: Given query is to find the position of the object at π.

Q: If the slope of the graph of f (same as slope of tangent line to graph of f), at the point (1, 2),…

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Q: Evaluate: S Vx(x - 5)dx

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Q: Let C1 be the curve with parametric equations x = cost, y = sint – t, where t e [0, 5]. (a) Find the…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x(2x + 5)8dx

A: Explained below

Q: Describe the graph of the equation. (8 – 21) i + 13rj r = O It is a plane in 2-space through the…

A: In this question we have to find point and nature of given vector.   Option d is correct.

Q: Find a power series representation for the function. (Center your power series representation at x =…

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Q: Fin volume of the object formed by rotating f(x)=1/x about the x-axis on the domain 1<x<infinity.…

A: We have to find the volume of the object.

Q: dy Suppose 2e-2* and y(1) = 4. dx What is y(2)?

A: Given,  dydx=2e-2x and y(1)=4

Q: The acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

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Q: Find x' for x(t) defined implicitly by x+t°x+t -8=0 and then evaluate x' at the point (-2,2).

A: x3+t3x+t4-8=0Differentiate w.r.t…

Q: {(1-9*"} bn a,b e R n

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Q: sin u cos v

A: This is a product to sum formula. This is a direct formula and here I m providing the formula onthe…

Q: sin x dx 1. V2-cos2x

A: integration

Q: Given the differential equation y'' – 4y' + 3y = 0, y(0) = 0, y'(0) - 2 Apply the Laplace Transform…

A: L yn = snY(s) -sn-1y(0) -sn-2y'(0) -...-sy(n-2)(0)-yn-1(0).

Q: 36 – x2 – y? and S2 be t Let Si be the hemisphere with Cartesian equation z = 6 – upper nappe of the…

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Q: In Exercises 1-3, find the general solution of the differential equation specifie lip 2. dt 1+t

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Q: 7 5 5. sec '(In t) tan° (In t) dt t

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Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

Q: 7. The ellipse with the equation y2 = 1 is rotated about the x axis to form a solid shape. A…

A: Given:  An ellipse:x252+y242=1  , rotated around x-axis. A cylinderical hole of radius 2cm along…

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: Evaluate the integral dx (6х + 5)? y making the appropriate substitution: u = dx (6x + 5)2 II

A: Given query is to find the integral.

Q: sec(tan(2x)) – 4 6. dx (cos(2x))? 8. / e*-* dx T e3x-e3x

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Q: Suppose that total cost is given by C(q) thousand dollars when q million units are produced. What…

A: Given query is to interpret the marginal cost C′(25) = 4.