A curve has Y= 4x + In (2x) for x>0, find the x coordinate of the point on the curve where the gradient is 3

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 9 sin(t). The initial…

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Q: valuate the integral Find the indefinite integral. √√₁+4x²³ (12x²) dx

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Q: Find the Maclaurin series for f(x) = 12e-x. What is the Maclaurin series of f(x) = 12e-x? n=0 (Type…

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Q: Identify the field below as conservative or not conservative. F = (9z +9y)i + (5z)j + (5y + 9x)k

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Q: Find all solutions of the given system of equations and check your answer graphically. (If there is…

A: We need to determine the solution to given system of equations graphically: 4x+5y=5-x-54y=-54

Q: Consider the power series: The interval of convergence goes from = -24 to z = 24 The radius of…

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Q: Find the exact area between y = x² and y = x for x ≥ 0.

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Q: [0,1] Find the maximum and minimum values of the function g(0) = 30 - 5 sin(0) on the interval…

A: For maximum and minimum then the first derivative is zero

Q: Determine if the series below converge absolutely, converge conditionally, or do not converge. 3. 80…

A: We know that the divergence test  If the absolute value of the limit is not equal to zero then the…

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. csc(x) = 4, tan(x) < 0 sin(2x) =…

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Q: The function f(x) = 2 + 4x +36x¹ has one local minimum and one local maximum. This function has a…

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Q: Explain why the derivative of y = logakx, k > 0, is dy/dx = 1/xIna for any constant k. (the a is the…

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Q: 10 Evaluate the integral. 3 2 Xx x-3 - 6x + 10 -dx

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Q: Find the exact value of the following expression using a sum or difference formula. 19T 12 cos O…

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Q: Consider the following. x = In(t), y = 9√t, t21 (a) Eliminate the parameter to find a Cartesian…

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Q: Rewrite In sin - In cos | as a s single logarithm and then simplify the result.

A: The expression is given as ln|sinθ| - ln|cosθ|.

Q: IJ 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2 3 4 Left endpoint Riemann sum for y = 2* on [0, 3]

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Q: iM8 (-1)" n-1 √n + 1

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Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

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Q: or the following function, determine intervals of concavity f(x) = x4 - 24x² + 11

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Q: Costas and Sheila bought a raffle ticket for a charity. The grand prize is $1000.00. Costa…

A: Costs and sheila bought a raffle ticket for a charity. And the grand total prize is $1000 Costa…

Q: What is the most general antiderivative for the function 8 32x³+ 8 + 5 O 8 6 5x5 2 x 3 - - 3x + C 3x…

A: given function is  f(x)=8x4-6x4-3antederivative of f(x) is F(x)→F(x)=∫f(x)dx

Q: Write the given expression as an algebraic expression in x. cos(2 tan-¹(x)) 1 -2x² (1+x²)² X

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Q: Determine the coordinates of the point P on the parabola y = 9 - ² that is closest to the point A…

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Q: Find the indefinite integral. (Use C for the constant of integration.) S -3 (+²+3)3/2 dx

A: Indefinite integral Where C is an constant

Q: 2. A company wishes to design a rectangular box with square base and no top. It needs to have a…

A: A rectangular box with open tob and square base  Volume= 27 cubic inches  Cost per square inches for…

Q: Use the method of Frobenius x²y" +4y'-2y=0.

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Q: 1 h(t) 0 6 1 0 2 3 53 65 4 60

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Q: Evaluate the limit lim f(t) where ƒ(t) = = lim f(t) = i 00-11 00-11 (9+17) 2 for t = 0.

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Q: -6 -4 3 31 6 5 4 3 2 -6 2 5 6 What is the period for the graph show above? What is the vertical…

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Q: Cost of Producing Guitars Carlota Music Company estimates that the marginal cost of manufacturing…

A: The marginal cost C'x=0.004x+110

Q: determine the absolute maxima and minima for following interval f(x) = 2x3 - 3x2 - 12x + 2 -6≤x≤5

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Q: 7 x8 Type your answer without fractional or negative exponents. Use sqrt(x) for √. Find the…

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Q: S6 (6x⁹ + 7x5) dx =

A: This by FTC WE GET

Q: The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management…

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Q: Determine if the series converges or diverges. Give a reason for your answer. Σ n=1 2n 9n-4

A: By divergence test if the limit value finite then the given series is diverges

Q: let a₁, a2 and a3 be the columns of A, let B = {a1, a2, a3} and let H = span(B).

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Q: Given the function f(x) = cos(2), compute the right Riemann sum R5 on the interval [0, 2]. R5

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Q: Find the indicated partial derivatives. f(x, y) = x³y - x7y8; fxxxx xxx XXX¹ fxxx(x, y) = fxyx(x, y)…

A: We know that the partial derivatives with respect to x then y is an constant

Q: The height, h, in feet of an object launched straight up after t seconds can be represented by h(t)…

A: The height h, in feet of an object launched straight up after t seconds can be represented by,

Q: 12 Evaluate the integral. 9 14 √(6x4-8) ¹4 9 dx

A: let  B=∫99(6x4-8)14dx

Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…

A: The solution is shown in step-2

Q: Identify the field below as conservative or not conservative. F = (9z+9y)i + (5z)j + (5y + 9x)k

A: The given vector field is:F=9z+9yi+5zj+5y+9xk

Q: Find the exact value of cos(u + v) given that sin u = Quadrant II.) and cos v = - 13. (Both u and u…

A: Given: sinu=725 and cosv=-1213.We need to find the exact value of cosu+v.It is also given that both…

Q: Question 2 Find the general solution of the equation (x² - x - 2) = x - 3y(x − 1) + 1. dx (a) (b)…

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Q: Find fx(x,y) and f(x,y). Then find f、(2, -1) and f(-4,3). f(x,y) = ex+y+3

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Q: Evaluate the integral by changing to cylindrical coordinates. √4-y² √4-y² [1 5 x² + y² xz dz dx dy

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Q: Find the particular antiderivative of the following derivative that satisfies th dy dx = 6x 2+5x +…

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Q: f'(x) = 4x³ - 12x² - 16x. (a) Find all of the critical numbers off. (b) Find the interval(s) where…

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Q: Step 4 Since u = 9x + 4, then converting back to an expression in x we get the following. (Remember…

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