1. For 1. For all n > 2, ¹n(n) >2, and the series Σ converges, so by the Comparison Test, the series In(n) ,2 converges. 1 n2

Q: A rectangle is inscribed in the region bounded by the graph of y= e1-2x^2  and have one of its side…

A:

Q: The net worth, f (t), of a company is growing at a rate of ƒ' (t) = 2000 - 121² dollars per year,…

A:

Q: Find the maximum and minimum values of the function f(x) = x The minimum value= The maximum value =…

A:

Q: Does the following series converge absolutely, converge conditionally, or diverge? ∞ Σ 1/2 4n n=1…

A:

Q: Suppose F(x, y) = (x + 2)i + (6y + 4)j. Use the fundamental theorem of line integrals to calculate…

A: Given vector field F=x+2 , 6y+4

Q: Compute the Riemann sum $4,3 to estimate the double integral of f(x, y) = 8xy over R = [1,3] × [1,…

A: Given that , fx,y=8xy and R=1,3×1,2.5 Calculate the Riemann sum S4,3=?

Q: Use the Root Test to determine whether the series converges absolutely or diverges. 4k² 8 Σ k=1 k…

A:

Q: A culture of bacteria is growing at the rate of 20e0.8t cells per day, where t is the number of days…

A:

Q: What is the x coordinate of the point where the graph of y=log2​(x+3)intersects the line y=4.

A:

Q: Suppose that the second derivative of the function y = f(x) is y'' = (x + 1)(x-2). For what x-values…

A:

Q: You are the marketing director for a company that manufactures bodybuilding supplements and you are…

A:

Q: Question 6 Use differentials to find the approximate value of y: (2x - 1) when x = 0.98. A 0.88 0.98…

A: Given; y:(2x-1)4, x=0.98

Q: Minimize the material needed to design a rectangular cubic box of volume 900 cm3.   Find the…

A:

Q: 5) Find all the complex cube roots of -8-8i.

A:

Q: Question 4 The radius of a circle is found to be 7 cm in length with a possible error of no more…

A: As we know the expression for the area of the circle is: A=πr2   ....(1) Where r is the radius of…

Q: Write the first four terms of the sequence {a} defined by the following recurrence relation. an+ 1 =…

A: We need to first four terms.

Q: dy at(5, 4) for the following by implicit differentiation: dx x6 = 36 2. Find

A:

Q: Consider the function f(x) = 4x² - 6x + 5, 0≤ x ≤ 6. The absolute maximum of f(x) (on the given…

A: We need to find absolute max and min.

Q: If f(x) = 7x² - x + 5 and h = 0, find the following and simplify. (a) f(x + h) (b) f(x+h)-f(x) h ||

A: a) Replace x by (x+h). b) Substitute the required.

Q: For f(x) = 2x and g(x) = x, find the following. (a) (f+g)(x) (b) (f- g)(x) (c) (f.g)(x) (d) (f/g)(x)…

A: For fx=2x and gx=x6, to find the following.a f+gxb f-gxc f·gxd fgx, x≠0

Q: Suppose F(x, y) = (4x – 2y)i + 3xj - and C is the counter- clockwise oriented sector of a circle…

A: The solution to find the circulation of the given problem is as follow.

Q: 8- Calculate R6 for f(x) = // on [2,4]

A: To calculate R6 for fx=34x on 2, 4.

Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(xy)], F = ▼ ƒ(x, y), and C is the segment of the parabola y…

A:

Q: Find the function represented by the following series and find the interval of convergence of the…

A:

Q: solve each inequality.   x2+x>0

A:

Q: Consider the graph of f'(x) below. At what value (or values) of x does f(x) have a local minimum? -6…

A: The solution is given below

Q: 1 - 3 2 a 1 To find the blue shaded area above, we would calculate: b [.. Where: f(x) dx = area 2 3…

A: Given query is to find the shaded area.

Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

A:

Q: A) Use Green's theorem to compute the area inside the x2 y² ellipse + 19² 14² Use the fact that the…

A: (A). Given       Equation of ellipse is - x2192+ y2142 =1...........(1)     Parameter form of…

Q: 4. Given x² + 9xy - 10y² = 0, Find the equation of the normal to the tangent line at the point (18,…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to x

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution.…

A: ∫xndx=xn+1n+1+cI=∫2x2x2-4dxd dx(xn)=nxn-1

Q: Use series to evaluate lim X→0 ex-(1+x) 4x²

A:

Q: Find the values of the variables. a +5 8z+1 11m 11k 3 a = Z= m = k = 3 }-{ 2a 4z 4m 8 - 35 75…

A:

Q: Evaluate the following geometric sum. 4 Σ 8k k=0 B

A:

Q: Nutrition   A certain company′s Mixed Cereal for Baby contains, in each serving, 80 calories and 10…

A: This is a linear programming problem. Here, we will first find the system of inequality, then graph…

Q: Evaluate the geometric series or state that it diverges. Σ n=0 ,-15n Select the correct choice below…

A:

Q: Show complete solution.

A:

Q: 1+tan² (0) = sec²0 49+ 49 tan² (0) = 49 sec ²4 (0) 49 + ( 7 tan (0))² = (7 sec (0)) ² Let x-1=7 tan…

A:

Q: Suppose f and g are continuous functions such that g(3) = 3 and_lim [3f(x) + f(x)g(x)] = 36. Find…

A:

Q: 8 Does the series Σ (-1)* - k=1 k k³ +2 converge absolutely, converge conditionally, or diverge?

A:

Q: a) Find the eigenvalues of A. b) Find three linearly independent solutions of x' = Ax. c) Find the…

A: The given matrix is; A= 2  0  0     -1   3  0      3   -3  0

Q: A boat is anchored offshore. From the bow of the boat, 40 ft of anchor line is out with 5 ft of line…

A:

Q: Consider the function f(x, t) = sin(x) sin(ct) where c is a constant. Calculate 2 f dx² of dt² || =…

A:

Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.

Q: Evaluate the indefinite integral. Stan ( tan³ (x) sec²(x) dx = +C.

A: We have to solve the given integration

Q: f (3 — e3x)3dx

A: The given integral is: I=∫3-e3x3dx   As we know the Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx And use the…

Q: Evaluate the line integral, where C is the given curve. √(x²y³ - √x)dy, C is the arc of the curve y…

A:

Q: A flu epidemic hits a college community, beginning with five cases on day t = 0. The rate of growth…

A: Given: rt=22e0·05t To find the total number of cases of flu in the first t days we need to find…

Q: In an effort to reduce its inventory, a warehouse runs a sale on its least popular Blu-ray discs.…

A: see below the answer and calculation

Q: Find the intercepts of the graph of 3x2 - 4y = 48.

A: