Test the series below for convergence using the Ratio Test. 4 0.5" T=D1 The limit of the ratio test simplifies to lim If(n)| where TL 00 f(n) = The limit is: (enter oo for infinity if needed)

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A: Solution is done in step 2

Q: he area is sketched below. ide the area below the curve into ple point of each rectangle. Ske AY

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Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: Find the sum. 59 4-5k Σ 9. k= 12 The sum is (Simplify your answer.)

A: I have appended the formula used in the solution part of the question

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Q: 3. (Extra) The Department of Health in a developing country has issued a warning that the number, N,…

A: Given problem:- The Department of Health in a developing country has issued a warning that the…

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A: The figure inscribed in the sphere is needed to be maximized. So, volume of cylinder is to be…

Q: Step 4 tan-(8x), then converting back to an expression in x we get u2 + C = 16

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Q: Find the indefinite integral. Hint: Let u = 3 - Vx. (Remember the constant of integration. Remember…

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Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

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A: Given query is to find the demand function.

Q: Let us model the number of automobile sales in a developing country as 151,000 N(t) t 2010 1+5.6e…

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Q: 11. Use the definition of the derivative to find f'(x) for the function f(x) = x2 + x + 2. Show your…

A: We have to find the derivative of the given function.

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A: Given problem:- find the volume of the solid that results when the region enclosed by the curves is…

Q: Evaluate: * dx re+1 5.) X-

A: Find your answer below

Q: 2x3-5x2+x+6 (b) lim 7x3+xー32

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Q: V9, 0< y< 4 Find the area of the surface generated by revolving the curve x = about the у-ахis.

A: We have to find the surface area.

Q: Find the equation for the tangent to the curve y = exp [2x] at the point (9, e 162). f(x) = exp [2x]

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Q: Evaluate the indefinite integral. (Use C for the constant of integration x3. x2 + 37 dx

A: Given query is to find the value of the integral.

Q: šin(3x) Find the area bounded by the curve y = ,0 <x<T/3 and the line y = 0 as shown 2+cos(3x) in…

A: This question can be solved using the concept of area under curve.

Q: 1)2xsin-13x

A: Given     write

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A: Question other than marked is also solved for your help.

Q: ||r(t) × r"(t)||. ||r(t)||* Use the formula k(t) : to find k(t). r(t) = t²i + t°j K(t)

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A: We have to find the roots of the given equation.

Q: Suppose log ,2 = a and log ,3= c. Use the properties of logarithms to find the following. log b…

A: Now,                logb1728b=logb1728+logbb=3logb12+logbbUse logbb=1.=3logb12+1

Q: A region is enclosed by the equations below. y = 2?, a = 3, y = 0 Find the volume of the solid…

A: We can solve this as follows:

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A: Given query is to find marginal cost function.

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A: Here, the given function is: f(t)=tt2-1 The function is not defined at x=1.

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Q: 2 dx 6) dx sec x csc x 7) -4tan x dx 8) -cot x dx

A: 1. ∫2sec(x)dxWe know that 1sec(x)=cos(x)=2∫cos(x)We know that ∫cos(x)=sin(x)=2sin(x)+C 2. ∫5csc…

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Q: can you explain the whole process, step-by-step? like in an essay type. how did they find the first…

A: Here the question is to find the first and second derivative of the function f(x) = 12cos2x. To find…

Q: For the given cost function C(x) 22500 + 600x + x², First, find the average cost function. Use it to…

A: For the given cost function Cx=22500+600x+x2, First, to find the average cost function. Then by…

Q: * This matrix is a 0 4 0 4 4 0 0 zero matrix square matrix diagional matrix unit matrix O

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Q: QS: Find the first derivative at x = 2 for the function given by the data 1.0 1.5 2.0 3.0 0.4057…

A: Solution: Given

Q: ||r(t) × r"(t)|| Use the formula K(t) to find «(t). r(t) = 5 cos(t)i + 5 sin(t)j + 4tk K(t):

A: Given rt=5costi+5sintj+4tkWe need to find kt by using the formula:kt=∥r't×r''t∥∥r't∥

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A: To find the length of the curve r=4 sin 2θ for π6≤θ≤π2.

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Q: Consider h(x, y, z) = cos (xy) + eyz + ln (xz). Determine the directional derivative of h at the…

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Q: Find the area of the region between the graphs of y = 13 – x² and y = over the interval 3 < x < 8. –…

A: Solve by integration

Q: Match each function with its power series representation. Functions: Power Series: Function 1: 2 1…

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Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Solving

Q: A farmer finds that if she plants 50 trees per acre, each tree will yield 55 bushels of fruit. She…

A: It is given that, If a farmer plants 50 trees per acre, each tree will yield 55 bushels of fruits.…

Q: If f(t) (0 , 01 Then find F(s) = f(t)e¯* dt where s>0 (simplfy your answer)

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Q: 8) A rectangular storage container with a square base is to have a volume of 2250 inches cubed. The…

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