Suppose we have the following sequence: An = n2+6n+4 an = 3- 2 - √n² +3 when n is odd when n is even (a) Write down a1, a2, a3, a4 (b) Determine if an converges or diverges. If it converges, give its limit.

Q: 2.4

A:

Q: Problem 1. (1) The integral 1 So + √√x(1+x)dx is improper in both ways we have discussed in class:…

A: Step 1: Evaluate the first integral Step 2: Evaluate the second integral Step 3: Therefore the…

Q: Let C be the curve parametrized by the equations.  x = e^2t - 2t, y = 4e^t (a) Find dy/dx in terms…

A: To find (dxdy​) in terms of \( t \), you can use the chain rule, given (x)and  as functions of (t).…

Q: ○ f(x) ○ g(x) 1. Compare the relative rates of growth of the following pair of functions and give…

A: Step 1: Step 2:

Q: 2. (a) Show that the following differential equation is separable: (x² - 1)y'xy = 0. (b) Use…

A: Ans 2 (a)Ans 2(b)

Q: (4) Using the fact that if f(x) ≥ g(x) ≥ 0, then √ +1 f(x)dx > N+1 g(x)dx, show that that diverges.…

A:

Q: I need help on question 6.

A: Here we get,v(3)=[−2(3)+9,(7−3)3/2,31​32−3]=3i+8j∣v∣=(32+82)​=73​Then the direction motion will…

Q: Find the accumulated future value of the continuous income stream at rate R(t), for the given time…

A: Part 2: Explanation:Step 1: Use the formula for continuous compounding to calculate the accumulated…

Q: No hand written responses. I need help with this equation that is at the very bottom. I need a…

A: Step 1:Step 2:

Q: Suppose R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y =…

A: To rewrite the iterated integral in the form dzdydx

Q: Find an approximation of the area of the region R under the graph of the function f on the interval…

A:

Q: Please see image

A: Thank you,Please rate my response.

Q: Find the point at which the line r(t) = <7, -7, -5> + t<5, -1, 4> intersects the yz…

A: For any query with the solution please ask in the comment box.

Q: Test the series below for convergence using the Ratio Test. n=2 In(n) 2n The limit of the ratio test…

A: Step 1:Step 2:

Q: Using the attached theorms, Solve dx/dt =10x-20y , dy/dt=8x-18y

A: solution to the given question is like this;first find eigen values and check they are real distinct…

Q: 6

A:

Q: Let u == (7,5,-5) and = (−1, −2, 2). Compute the following: u v . . = 2 7(ū. v) = (7) · v = ū. (77)…

A:

Q: *Use First Derivative Test

A: Let length be x meters and breadth be y meters.xy=1200y=x1200​Total cost of fencing is…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: Step 1: The formula for average rate of change is ΔTΔF​=b−af(b)−f(a)​ Step 2: the formula for…

Q: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x²+z² and y =…

A: Step 1: Step 2: Step 3: Step 4:

Q: == Over the next 10 years, a company projects its continuous flow of revenue to be R (x) = 90e0.15…

A:

Q: Given the following information, find the matrix A. (1/17) = 10 Instructions for the answer: Type…

A:

Q: 2.7

A: Step 2: Step 3: Step 4:

Q: Find the indefinite integral. (Use C for the constant of integration.) [sin(3x) cos(3x) dx

A:

Q: Find the dimensions of a rectangle with an area of 144 square feet that has the minimum perimeter.…

A:

Q: n=1 8n +2n gn

A: Step 1: State the given summation: ∑n=1∞​9n8n+2n​ Step 2: Expand the summation:…

Q: 4. 5

A: If you have any problem let me know here in comment box for this thankyou for your question.

Q: Determine whether the statement is true or false. True False If Σ C_8" is convergent, then Σ C^(-4)"…

A:

Q: ☐ ☐ 1. Approximate the following integrals using Simpson's rule. (Round answer to three decimal…

A: Step 1: So, the approximate value of the integral is 0.130 (rounded to three decimal places). Step…

Q: Test the series below for convergence using the Ratio Test. n= n72n 5n-1 The limit of the ratio test…

A: Given the series,n=1∑∞​5n−1n72n​ Using ratio test to test for convergence of the series, we…

Q: x = e^2t - 2t, y = 4e^t  ,  t= ln2 (c) Find the times t where the tangent line is vertical. If the…

A: (c) To find where the tangent line is vertical, we need to find where the derivative of x concerning…

Q: Application 19. Determine the derivative of the following & simplify (within reason): [ a)…

A: Thanks for your patience!Kindly comment if you need any clarifications.

Q: ← www-awu.aleks.com/alekscgi/x/Isl.exe/10_u-lgNslkr7j8P3jH-IB-d4xj11 PLIKACnhGTWihclRH MCSD…

A: (a.) The given percentage in the sentence is: 7% Recall that a percentage is a number expressed as a…

Q: 5 √² Using the method of u-substitution, (4x-7)² dz- f(u) du where u = du a = b = f(u) == The value…

A: Given:I=∫25​(4x−7)2dxLet u=4x-7Therefore,dxd​(u)=dxd​(4x−7)dxd​(u)=4dx=4du​Also,u=4x-7, when x=2,…

Q: Consider the function f(x) 2 10 = x2 x6 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A: Step 1:Step 2:this is the continuation of above image  Step 3: Step 4:

Q: -1 csch¹x = ln √1 + x2 x % 0 x |x| Prove mathematically that the right-hand side is equal to the…

A: Steps of the proof are as follows:In case of any doubt, please let me know. Thank you.

Q: Sketch a graph of the polar equation and find the tangent lines at the pole for 0 ≤ 0<π r = = 3(1 -…

A: Step 1: Analyze the Polar EquationThe equation r = 3(1 - sin(θ)) defines a relationship between the…

Q: Problem 4 - Transshipment - Grandma's Cheese Shed (15%) Your team has recently accepted a consulting…

A: Grandma's Cheese Shed is struggling to keep up with the demand for their new spicy cheeses. To…

Q: 10

A: Detailed explanation:

Q: coth-1 x = tanh 1 x 1 x Prove mathematically that the right-hand side is equal to the left-hand side…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: | | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a)…

A: Step 1: Step 2: Step 3: Step 4:

Q: Over the next 5 years, a company projects its continuous flow of revenue to be R (x) = 90e0.15x…

A:

Q: The area R in the plane is bounded by the curves given by (x = y^2 + 2), (y = x - 4) and (y = 0), as…

A:

Q: on Given the system below, -8x+ay = 4 3x + 2y = -1 find: 1. Value of a, if det (A)=-1 Instructions…

A:

Q: (7 and 8) Explain how to solve these question in detailed steps.

A: QUESTION 7: We're looking for where the function f(x) is concave up on the graph provided. A…

Q: 4) At t=0, a rock is thrown down from the top of a 100 m tall building with a downward speed of 5.0…

A:

Q: Please help me with these question. SHow all you work. Thank you 1. Prove that∀k ∈ N, 1k + 2k + · ·…

A: The first question is asking us to prove that the sum of the kth powers of the first n natural…

Q: Use the table graph to answer question in photo.

A: Step 1: Step 2: Step 3: Step 4:

Q: Given f(x, y) = -x-6x²y²+ 3y3, find 22 fx(x, y) = fy(x, y) = for(x, y) fry(x, y) =

A: Step 1: Step 2: Step 3: Step 4:

Q: S₂ S Now Ꮖ (xy+5) dydx try the integral X dady to see why the order of integration is important.…

A: To solve the double integral, we first integrate with respect to y: ∫27​[−7(xy+5)71​]34​dx This…