Obtain the sum of the seri Ean $a = -² 2 n=2 nn

Q: Differentiate the function with respect to the independent variable. x f(x) = 4x cos+ + cos f'(x) =…

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Q: 6 1-x² dx

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Q: Use the shell method to find the volume of the solid formed when a hole of radius 1 is drilled…

A: We have to solve above problem.

Q: State the order of the given ordinary differential equation. (1-x)y" - 3xy' + 6y = cos x Determine…

A: Order = highest derivative order = 2

Q: Show that the interval [a,b] is complete

A: Given

Q: Aw 2.f(x) 4 3. f (x) = x 9 =

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find two numbers whose sum is "a", if the product of one to the square of the other is to be a…

A: sum of two numbers is 'a', the product of one to the square of the other is to be maximum

Q: 18. The solution of the differential equation 2xy = x² + 3y² when y(1) = 3 is dx

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Q: Question 9 Evaluate: lim1 (3-2x)tan (37) O e O None of the choices 01 e 3r O ∞

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Q: Given F(x) below, find F'(x). et -1₁° 0 F(x) = (1³ + 7) dt

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Q: Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2)…

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Q: en the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q² − 2Q³…

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Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: f(x) g(x) XX 2 5 6 7 The graphs of the functions f and g are shown below. If h(x) = Y A Provide your…

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Q: 1 Suppose that I is a location function of an object, given as L(t) = We will compute the 3t - 7…

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Q: 2. Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ = x + y = 0 (b) x…

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Q: 2. Find d using implicit differentiation. Enclose final answers. dx (a) √x=y=√√√x + y = 5 (b) xsin y…

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Q: 5.494949... = 5. 49494 100000 X

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Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

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Q: Find the area moment of inertia with respect to x of the plane region y=9-x^2 bounded by the…

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Q: Find the area of the surface generated when the given arc is revolved about the y-axis ㄷ y = 4 - x²…

A: We have to find area of the surface .

Q: Find the first four derivatives of the following functions: 1. y = 4x³ + 12x² + 7x 2. y = 2x5 + 6x²…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the value of k so that the given differential equation is exact. (y³ + kxy4 - 2x) dx + (3xy² +…

A: Given differential equation is (y3+kxy4-2x)dx+(3xy2+20x2y3)=0

Q: 1. f(x) = 3ex +1 2. f(x) = 45x + x45 3. f(x) = 10 sin x + 5 sec x 4. f(x) = x²(2x + 1)

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 2 S² T ㅠ 1-cos x dx 2

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Q: Find the number in the interval [0,3] such that the difference of its square from its cube is the…

A: Given problem:- Find the number in the interval [0, 2/3] such that the difference of its square from…

Q: When fully multiplied out, what is the 8th term of (x-3y)¹2?

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Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 8, f'(9) =…

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Q: What is the volume of the solid formed when the region bounded by the curve y =√16x², x = -3 and x -…

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Q: f(x) = 45x6

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Q: TC Find the area of the region bounded by y = cos x, y = 1, and x = =

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Q: Find the value(s) of k that makes the given function continuous. (-x+2 if x < k f(x) = 4x + 3 if k ≤…

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Q: Find the average rate of change of from y = x³ - 2x + 3 from 0 to x = 3. -

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Q: 2X 4) y = C₁ + c₂e² c + C3 e-3x

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Q: T/6 6 tan 2x dx

A: In this question, we need to evaluate the given integral.

Q: Find dy dx In y = e sinx O dy dx O dy dx O dy dx O dy dx = yey sin x =yey cos x = 4 1- ye cos x yey…

A: We can find the answer as below.

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: Let's solve.

Q: a. Find the lengths of the sides of a rectangle whose perimeter is 40 cm and whose area is 75cm².…

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Q: 2 X 2 - a² dx X

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Q: ∫0.00202003x^4/4-0.0185672x^3/3-0.0937054x^2/2+2.17676x+C

A: We have to solve it. But it's not clearly mentioned that, either We have to find integration or…

Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

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Q: An open-top box is to be made from a 12-inch by 18-inch piece of plastic by removing a square from…

A: We can find the value of x by using the second derivative test.

Q: Find F(s). ℒ{t3e−4t}

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Q: Find the normal line to f(x) = ax² - 4ax at x = 3. Assume that a is a positive constant. Next…

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Q: Question 4 Find two numbers whose sum is "a", if the product of one by the cube of the other is to…

A: To find out two numbers.

Q: Question 3 A container with square base, vertical sides, and open top, is to be made from 3,000 ft²…

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Q: Find the derivative: y = x [ln(x) - 1] O ln(x) - 1 о O x ln(x) O In(x) O 1 + In(x)

A: Given y=x[lnx-1]To find dydx:

Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.

Q: + 75 3-4x Evaluate lim x-4 1 -4x-6 + Enter an exact answer. Provide your answer below: 13

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