Determine whether the series is absolut Σ n = 1 sin(n) 57 O absolutely convergent conditionally convergent O divergent

Q: The graph of f(x) is given below. On what interval(s) is the value of the derivative f'(x) positive?…

A: To find out the interval in which the function is increasing or positive.

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: 38. A rectangle is inscribed in a semicircle with diameter 10 centimeters as shown. Express the area…

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Q: Q.1: Solve the differential equation below; xy' + 4y = 8 x4

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Q: Solve the differential equation by variation of parameters. y" - 2y + y = et arctan(t) y(t):

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Q: Find the average value of f(x) = Enter the exact answer. fave = x (6x² + 5)² over the interval [0,…

A: Avg value is given by below

Q: an+1 Suppose that an Σ an( – 36)" x2n n=1 → 1 as n → ∞o. Find the radius of convergence.

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Q: Let g(x, y, z) = xy + yz + zx. Find a nonzero vector perpendicular to the level surface g(x, y, z) =…

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Q: QUESTION 13 Is this true or false? The radius of convergence for Σ()" n=0 is R = Show why your…

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Q: 3. Find the average rate of change of function f(x) = 4 - 2x² (a) On [0, 1] (b) On [a, a+h].…

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Q: Use the graph below to write the quadratic function in vertex form. Be sure to use the equation…

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Q: 150 Find the consumers' surplus for a product if the demand function is given by D(x) = 3+x Answer…

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Q: y=-3 x=- V25 – x – y dxdy=

A: To solve the following double integral

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 6 x+8 dx Write your answer exact…

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Q: (d) A√x X²-2 3z +9 use quotient Rule use quotient Rule

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Q: Tutorial Exercise Evaluate the definite integral. I [²² sin5(x) dx Step 1 To solve the integral…

A: We have to integrate the given term.

Q: 3 2 X'+X +2x + 30 - 2 (22-3x+29 2) -dx

A: Let's integrate given integral.

Q: = Consider the region B under the graph of y x = [5,7], and above the x-axis. 2² +7 x+5 J Estimate…

A: We want to find estimated area using left and right endpoints.

Q: 14. Given the function f(x) = 3x³ – 48x find the following: (Round to 1 decimal place) a) The x and…

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Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: Consider the equation below. (If an answer does not exist, f(x)=x²-x-In(x) (a) Find the interval(s)…

A: We have given a function and finding point for local minimum value

Q: Let R be the region bounded by y=x, x= 1, and y = 0. Use the shell method to find the volume of the…

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Q: Use the cross product to find the area of the parallelogram whose vertices are (0,0,0) , (0,2,1),…

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Q: Problem 3. The rate of consumption of hamburgers in Wyoming (in millions of hamburgers per year)…

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Q: Find dy/dx, given that xy^3 -3y^2 +xy=1-3x

A: We have given a function y in term of x, and finding the derivative of that

Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

A: The function is given as , fx=8x33+14x2-16x find the location and value of the absolute extreme…

Q: 2. At a local maximum point f '(x) = 0. a) always b) sometimes 3. If f '(x) = 0, then the point (x,…

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Q: Find r'(t) r(t) = e-ti + 7j + 4teck r'(t) = (No Response) Need Help? Read It Watch It

A: Let's find derivative of given function.

Q: An open-top box is to be made from a 18-inch by 42-inch piece of plastic by removing a square from…

A: Diagram of the mentioned box will  be as following

Q: (a) Find Maclaurin expansions for sin 2x, cos 2x and e³ up to and including the term in x³. I (b)…

A: Maclaurin Series for f(x) :       f(x)≈ f(0) +f'(0)x +f''(0)x22!+f'''(0)x33!+... Note : As per our…

Q: onds and S(1) is the distance in feet from the top of the building. What was the average speed of…

A: topic :- application of algebra

Q: (2,-1,0), B(3, 0, -2), and C(0, -3,-1). ) Find the equation of the sphere with center C nd radius…

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Q: Apply the rule of integration by parts. -S Sudv. dv = uv - du = Let dv= ew dw and integrate the…

A: Here we will fill all blacks of prat 2 as shown below

Q: In the plane R², consider the parametric curve given by the equations Jx(t) = cos(t) + 2 y(t) =…

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Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and 6=. (a) Find the unit vector u…

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Q: 7. Suppose the equation əz ar is a differentiable function of r and y implicitly defined by 2³ = y²…

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Q: Solve the given IVP using Laplace transforms. x" - 2x + x = 2tet x(0) = 0, x'(0) = 0

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Q: Find the critical points of the given function. 5. f(x) = 2/3+2/3 +x-2/3 6. f(x) Va 7. f(x) (3x +…

A: Given: 5)     fx=14x43+x13+x-23 After simplifying we get     fx=14x43+x13+1x23 Critical points:…

Q: Find the relative rate of change. Evaluate the relative rate of change at the given value(s) of t. -…

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Q: A In 14x²+2x+11+ C B 2 In 14x2+2x+11+ C 4x+1 4x²+2x+1 D dx In 14x²+2x+11+C 3 In 14x²+2x+11+ C 4

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Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

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Q: Consider the graph of f'(x) given below. At what value(s) of x does f(x) have a local minimum? If…

A: we have given the graph of f(x) we know that at maxima and minima f'(x) =0  (means slope at that…

Q: This is the approximate time right ? Making the no. of days from feb to aug into 30, by that logic…

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Q: c) [. The intersection of the sphere B and the xz-plane is (x - 2)² + (z + 1)² 2)² + (z + 1)² = 9.…

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Q: 7. The points of inflection are found by solving the first derivative equal to zero. 8. When the…

A: You must have idea about Calculus in order to get the answer for these questions.

Q: A 2x-In Ixl+C B 2x4 In Ixl+C 5*²=4 dx x D HIN x² - In Ixl+C x² - 4 In 1x1+C

A: topic- indefinite integral ∫xndx=xn+1n+1+C∫1xdx=lnx+C

Q: Use differentials and the graph off to approximate the following. (Round your answers to two decimal…

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Q: Let [ 13.5 f(x) dx = 8, 45 f (a) f(x) dx = 3 J4.5 9 (b) (5f(x) - 2) dx = J4. f(x) dx = 3, and Enter…

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x. 32 y = 9x, x…

A: Given that Y= 9x - 32/x ; x= 4. And we find curvature and curvature of the plane at give x value.…

Q: Find the largest interval centered about x = 0 for which the given initial-value problem has a…

A: We have to find the largest interval centered about x = 0 for which the given initial-value problem…