1. Given the following expression: 27 81 3 9 + + 10 100 1000 10000 a) Using sigma notation, write the expression as an infinite series. b) Find the partial sum S5. + + c) Determine if the series is convergent or divergent. If it's convergent, find its sum.

Q: Find the general solution of the differential equation. y(4) + 12y" + 36y = 0. NOTE: Use C₁, C2, Cs,…

A: We Have to find general solution of given Differential Equation.

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Q: et f(x) [8− x − x² if x ≤ 2 12x - 5 if x > 2 Calculate the following limits. Enter "DNE" if the…

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Q: 1. Does the definite integral [a,b]? Why or why not? 2. How would you calculate the total area of…

A: Here we have to use the concept of integration

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Q: Σ 2-In(n) n = 1

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Q: 6. у” – 5y' + бу = 0 I

A: We have to find the general solution of differential equation

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Q: Use the integration capabilities of a graphing utility to approximate to two decimal places the area…

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Q: $ S®- floor't. & сод

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Q: When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the…

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Q: r- 24. y" +9y = 0; y(0) 25. y"-2y' + 2y = 0; 26. y" - 2y' + y = 0; 27. y"" - 4y" + 7y' - 6y=0; = 1,…

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Q: Determine the intervals in which solutions are sure to exist. t(t2)y(4) + e'y" + 9t²y = 0 Enter the…

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Q: Determine whether 65"+¹ is convergent or divergent. O divergent O convergent a=1

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Q: The reproduction function for king salmon in a sea is f(p)=p² + 7.5p, where p and f(p) are in…

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Q: Question 1 ť 2,0 5 -12 Use the graph of f(x), shown here, to determine the limits, when they exist.…

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Q: Evaluate the following integral or prove it divergences ez [Fot e²x + 3 da

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Q: FL Find the cross product u x where = 7i+8j +4k and 7 = (5,- 9, 2). u xv= Question Help: Video…

A: To find u×v use the following formula

Q: 9. 23/2 3√x+1 - S dx

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Q: Find three first order partial derivatives of the following function. f(x,y,z)=(x/y)*sin(z)

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Q: In each of the problems, apply the method of reduction of order to find a second solution of the…

A: The given differential equation is:x2y''+3xy'+y=0, x>0:The given solution is y1x=x-1=1xWe need to…

Q: In each of the problems, apply the method of reduction of order to find a second solution of the…

A: We have to solve given Questions.

Q: =(4,-1, 7) along b = (6, 6, -7) and the vector component of v Find the vector component of v =…

A: Given vector,v = 4, -1, 7b = 6, 6, -7Vector component of v orthogonal to b.

Q: ve the separable differential e C 1 = x² + t d find the particular solution sa 0) = = - 2.

A: topic;- application of integration

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Q: Let f(x) = x^2 + 3x^2 + 9. d) The absolute maximum value(s) of f(x) and the absolute minimum…

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Q: Approximate the value of y2(2) using the method of successive approximation for the given…

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Q: DUE NOW! Answer only. Thanks Determine whether the statement is true or false. If  f and g are…

A: Given : f(x) and g(x) are discontinuous at x = c then we want to find out that f(x) + g(x) is…

Q: Solve the given initial-value problem. y(x) = 4y" - 4y' 3y = 0, y(0) = 1, y'(0) = 3

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find the directional derivative of the function at a given point in a unit direction.

Q: C Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos(ex) y(x) =

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Q: [Fid F. dr, where C is given by the vector function r(t). C F(x, y, z) = (x + y2) i+xz j + (y +z) k,…

A: NOTE: Refresh your page if you can't see any equations. here we have ................(1) so we have…

Q: find the vertical asymptotes of the graph of the function f(x)=ln(x+3)

A: x=a is said to be a vertical asymptote of a function y=f(x) iff as x tends to a f(x) tends to ∞ or…

Q: 6r (x²+3)²¹ 14. Given f(x). f'(x) = ²+3 (m). Write "none" where appropriate. (a) Domain of f: (b)…

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

Q: 1. Explain what it intuitively means for function f(x,y) to be continuous in some domain D.

A: To explain the meaning of the given statement.

Q: Find the Cartesian coordinates of the given point: (r, 0) = (√3, 4). OA) (₁ (1/2, 1/³) 2 ○ (³,²) B)…

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Q: Find the limit, If it exists. (If an answer does not exist, enter DNE.) x² + y² lim (x,y) → (0,0) x²…

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Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: You know that d/dt f(r(t)) = 69 at t=7 if r(t) = [t, t] and d/dt f(r(t)) = 21 at t=7 if r(t) = [t,…

A: Given that , ddtfrt=69 at t=7 if rt=t,t and ddtfrt=21 at t=7 if rt=t,14-t find the gradient of f at…

Q: What is the distance between the point (-2, 5, 3) and the z-axis?

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Q: 1. Integrate: a. (2x²+3)¹/²+c b. (2x²+3)² +c c.(2x²+3)³/²+c d. 2(3x²+2)¹/2+c

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Q: 1. For the following sequence, give an explicit formula for the nth term. 4 9 16 25 36 49 1' 3'9…

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Q: 42 1. Calculate the Laplace transform of f(t) = 1. 2. Calculate the Laplace transform of f(t) =…

A: Let's find laplace transform.

Q: Find the missing values by solving the parallelogram shown in the figure. (The lengths of the…

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Q: If a ball is thrown vertically upward with an initial velocity of 96 ft/s, then its height after t…

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Q: The solution and answers are incorrect

A: The correct solution is given below

Q: Express the number 3√3 - 6i in the form R(cos(0) + i sin(0)) = Re¹0, where R> 0 and -T≤ 0 ≤ T. NOTE:…

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Q: The graph of the second derivative f"(x) is given below. On what interval(s) is the function f(x)…

A: NOTE: Refresh your page if you can't see any equations. . the function is concave up when  as we…

Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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