Write the expression 4(sin(2x) − cos(2x))  in terms of sine only.

Q: A cylindrical can has a radius of Sº, a height of h and a slip-on lid of fixed length a. If the can…

A: Radius of the cylindrical can = rHeight = hLength of slip-on lid = aCan and its lid are made from A…

Q: f(x)=x²-2 g(x) = 3x +5

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Q: Find all vertical asymptotes of the following function. f(x) = 2x + 10 x² - 16

A: To find all vertical asymptotes of the following function.

Q: Suppose that a colony of beetles grows exponentially with doubling time 7 years. How many years does…

A: The objective of this question is to find out how many years it takes for a colony of beetles, which…

Q: Using only improper integration, please evaluate the following integral: dx (3x + 1)²

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Q: Find the average rate of change of the function over the given intervals. h(t) = cott 3 5T a. b. 5…

A: Average rate of change of f(x) over [a,b] is given by average rate of change of f(x) =

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: A company makes portable heaters for outdoor dining. The company has total cost function C(x) =…

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Q: Find the radius of convergence for ∞ n=1 n! -xn. 1·3·5· ... · (2n – 1) · (2n – 1) x²

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Q: Find the derivative of: -7e-3* cos(-9x). [Hint: use product rule and chain rule!] Use e^x for e*.…

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Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: 7. DETAILS SPRECALC7 7.2.017. Use an Addition or Subtraction Formula to write the expression as a…

A: Let,.We know that,

Q: Find the Riemann sum for f(x) = x² + 3x over the interval [0, 8] (see figure), where Xo = 0, x₁ = 1,…

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Q: Find the derivative of the following function. You do NOT need to simplify your answers. f(x) = e*…

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Q: Determine the area of the given region under the curve. y 2

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Q: Suppose that the total cost (in dollars) for a product is given by C(x) = 1400 + 150 ln(2x + 1)…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: As per guidelines, we can solve only first 3 subparts if multiple subparts are posted. Please repost…

Q: Given the two planes, find an equation of their intersection, if any. If the planes intersect, find…

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Q: - Some books say that / csc(x) dx = Ln|csc(x) − cot(x)| + C, while other say that [csc(x) dx =…

A: The given integral is

Q: Solve the integral: f sin(2x) cos(3x) dx – do NOT use the "product to sum" identity for this, even…

A: Wr have to evaluate the integral without using product to sum identity

Q: Derive the formula for the derivative of the inverse cotangent function. Please show all step

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Q: Solve the integral: § sec2(x) tan(x) dx two different ways: By letting u = sec(x), and by letting u…

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Q: Use implicit differentiation to determine dy dx || dy dx given the equation x² + y³ = sin y.

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Q: Find the curl of the vector field F = (2y cos(x), 7x sin(y)). curl F-

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Q: 6) Differentiate: a) y = 2x - x² tanx

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Q: 8. Evaluate the integral. 장 T x + 1 x2 + 2x -dx

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Q: Suppose f is a differentiable function. If f(6) = 7.9 and f'(6) = 6.1, then estimate the value of…

A: The objective of this question is to estimate the value of the function f at the point 6.4 using the…

Q: (*) O The points (3, 0), (x, 0), and (3, 1/x2) are vertices of a rectangle, where x ≥ 3, as shown in…

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Q: Find the indefinite integral. Check your result by differentiating.      8x dx

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Q: Given that ∫72f(x)dx=5111, what is ∫27f(s)ds?answer =

A: The objective of the question is to find the value of the integral ∫27f(s)ds given that…

Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. x³ +y³…

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Q: Find all horizontal asymptotes of the following function. f(x) = 3(x − 1)(x + 1) 2(x - 1)

A: f(x)= 3(x-1)(x+1)/2(x-1)We have to find horizontal asymptotes

Q: After we apply the Laplace transform to the equation y"-2y'+2y=e', given the initial condition y (0)…

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Q: Find the center of mass of the laminas in the figures below obtained by removing squares of side b =…

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Q: Find the arc length of y = 2x + 4 on 0 ≤ x ≤ 4

A: The given curve .The aim is to find the arc length of the curve in the interval .

Q: Find the area in the third quadrant bounded by the curve y ·x³ + 5x² -x-3.

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Q: a) Approximate Ĵ; dx using left Riemann sum with 4 equal subintervals. 10 2x+1 b) Calculate the…

A: The given integral The Left Riemann sum

Q: 1. Find the tangent line to the curve r(t) = at (0, 1, 0). 2. Find tangent line at t = π/4.

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Q: Write out the first four terms of the series to show how the series starts. Then find the sum of the…

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Q: (b) Determine whether the sequence converges or diverges. If the sequence appears to converge, find…

A: we have given sequence

Q: Rearrange the equation to solve for x. a = h(c+x)

A: a = h(c+x)

Q: 5. (A) 2.2 (B) 2.8 (C) 3.4 (D) 3.8 (E) 4.6 Consider all right circular cylinders for which the sum…

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Q: 1 4 √x 5 18 dx =

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Q: dx 4. √ (sec 3x)√1-cos² 3.x S

A: 1/secx = cosx 1-cos2x = sin2x cosx/sinx = cotx

Q: path r(t) = (t)i + (t²-7) j describes motion on the parabola y=x²-7. Find the particle's velocity…

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Q: 2 AC X3 M13 The endpoints of segment AB are A (5,7) and B-2, 11, (a) Find the Midpoint of AB, (b)…

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Q: John sees Hua running towards him at 11 m/s. While running, Hua throws a ball to John at 5 m/s. What…

A: Speed of Hua = 11m/sspeed of the ball = 5m/s

Q: Find the Taylor series for f(x) centered at c. 1 7x f(x) = f(x) = ∞ Σ n = 0 C = 8

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Q: 2. Evaluate the following indefinite integrals: [x² In(x) dx [x²e* dx a. b. C. fxcos(3x) dx

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Q: Why would x equal sin(t)?

A: The given integral,