A man wishes to use 141 feet of fencing to enclose a rectangular garden. Determine the maximum possible area of the garden.

Q: Find the Maclaurin series for f(x) using the definition of the Maclaurin series. f(x) = xcos(5x) M²…

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Q: Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x…

A: The answer is given below:

Q: Eliminate the parameter to express the following parametric equations as a single equation in x and…

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Q: Let f(x) = x² g(x³). Suppose g(64) = 7, g(48) = -4, g' (64) = 4, and g' (48) = -3. Find f'(4) =

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Q: Find the arc length of the following curve on the given interval. x = 71³, y=21², osts √/3

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Q: 6. Use the graphs of f and g to find the function values: 4 3 2 2 (a) (f + g)(4) f(x) 3 3 2 1 (b)…

A: Given:

Q: Solve the given differential equation. e5x -5ydx-dy = 0

A: e5x-5ydx-dy=0 this can be written as  e5xdx = e5ydy now apply integration both side we get ∫e5xdx =…

Q: (b) √√√√x+2 − x|dx -

A: NOTE: Refresh your page if you can't see any equations. . the given function is  so first we need…

Q: The Taylor series for f(x) = eª at a = -4 is Σ en (x + 4)". n=0 Find the first few coefficients. CO…

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Q: using Part 1 of the Fundamental Theorem of Calculus. Remember to include a "+ C" if appropriate. √²…

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Q: mizing Construction Costs An open rectangular box is to have a volume of 768 ft³. If the material…

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Q: Determine whether the improper integral converges or diverges, and if it converges, find its value.…

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Q: Find the average value of f(x) = x³ on the interval [3, 5].

A: Given function, f(x)=x3 on [3,5]

Q: 6) Show that (2xy, y, 2yz + + x², y²) is conservative.

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Q: Find the Taylor polynomial T3 (x) for e^3x centered at 0. What is T3 (1)?  (T3 is suppose to look…

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Q: Given that 1 - X 2x8 n=0 X = 1 to x = X ∞ n=0 with center 0. Identify its interval of convergence.…

A: The answer is in step 2.

Q: Given the acceleration function (in m/s2) for a particle moving along a line, find (A) the velocity…

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Q: Give a possible formula of minimum degree for the polynomial f(x) displayed in the figure to the…

A: To determine the formula for the polynomial whose graph is given.

Q: Consider the differential equation (a) Find 71, 72, roots of the characteristic polynomial of the…

A: According to question,Given Differential equation,y''-3y'+2y = 0

Q: Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

A: (5) Evaluate the Laplace transform Letsin2t=?

Q: solve for the variation of parameter of: y''+y= tan(x)

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Q: 6 6 Suppose f(x) dx = 9 and f g(x) dx = −8. eff (2) d +¡¸g(= -5 -5 6 Evaluate (-2 f(x) + 2 g(x)) dr.…

A: Given:- ∫-56fxdx=9  and ∫-56gxdx=-8

Q: Find the arc length of the following curve on the given interval. K|N x=6 sint-6t cost, y=6…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: Use the integration table to find the indefinite integral. (Use C for the constant of integration.…

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Q: Find how fast the volume of a parallelepiped is increasing if its edges a, b, and c change at rates…

A: According to question,Given Data,edge of parallelopiped,a=3 units,b=10 units,c=6 units,andRate of…

Q: A pizza pan is removed at 4:00 PM from an oven whose temperature is fixed at 425°F into a room that…

A: Let's find temperature by using Newtons law of cooling.

Q: xy' + y = x² - 3x

A: xy'+y= x4-3x

Q: (g) Sketch the triangle and solve for all missing values in the triangle using the Law of Sines. ZB…

A: Let's solve triangle.

Q: Compute the percent relative error in computing the area of a square whose side is measured with an…

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Q: 2. Estimate the area between ( the curve y = x² + 1 and the x-axis over the interval [0, 4]. Use a…

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Q: Given the definitions of f(x) and g(x) below, find the value of (fog)(1). f(x) = -3x - 14 g(x) =…

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Q: 1 x² - 4x +3 2 X Critical points at .x=0, x= 1, x=2, and x = 3 Critical points at x = 1, x=2, and x…

A: this is question of algebra  here we have to find the critical point of curve function  further…

Q: Find the value of the limit for the sequence given. 1-9-17 (9n+1) 0 -1 I 9n+D)} öö (9n)²

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Q: Given its bounds: z = 4 - y2, z = 0, x = 0, and x = y, find the volume of the solid using integrals.

A: The given curves are: z=4-y2,    z=0,   x=0  and  x=y

Q: 5. t dx dt = 6te2t + x(2t - 1)

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Q: Calculate the following derivative: f d dx cost+t²dt

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Q: ³ f(42° +22³) dz Find + C

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Q: 2. Consider a toy of density p(x, y, z) = z given by the region bounded by the paraboloid z = x² +…

A: Let's find mass of toy.

Q: Find the radius of convergence and the interval of convergence of the power series (2x)" 72! R=2,…

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Q: (c) Triangle ABC has a = 7 in; b = 8 in and c = 10 in. Solve for cosA. Answer: cos(4)- 23/32

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Q: 2x²ydy where C is the triangle with 7) Evaluate Sexy² dx vertices (0, 0), (2, 2) and (2,0)

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Q: Suppose that p(x) X = = to x = n=0 convergence of p(9x − 2). " ∞ anx converges on (-1, 1], find the…

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Q: 5. Find the derivative of: A) y = 2* B) y = 4 x² +3

A: Solution ⇒    5(A) y=2x    We have formula of derivative that is,…

Q: A point is moving along the circle x^2+y^2=r^2 in the first quadrant such that its x-coordinate…

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Q: Find the integral. Show work. fx¹nx dx 25 (51nx-1) + C 1 25 (lnx-1)+C Ox++0 x(51nx-1)+C

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Q: Use a calculator to evaluate the following expressions. Round your result to three decimal places.…

A: NOTE: Refresh your page if you can't see any equations. . using the calculator, find the value of…

Q: Assume y is related to x through the differential equation: a =b-y dy dx where a = 0.2, b = 1.4,…

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Q: 2y 8. y' — ² = x²ex ; x = 1 when y = 0

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Q: The characteristic equation for the differential equation: d² x dx a +b. + cx = 0 dt² dt has complex…

A: Given a differential equation