(a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 6 x+8 dx Write your answer exact and also 3 decimal places accurately. (b) Use the Fundamental Theorem of Calculus to evaluate the integral S.³ dx 8 x-6 x+8 (c) Discuss/compare your findings in part (a) and part (b)

Q: Use an area formula from geometry to find the value of the integral by interpreting it as the…

A: Find the value of integral

Q: Consider the double integral f(x,y)=(x²+y2) 3/² over the region R where y is bounded between 0 and…

A:

Q: Given f(x)=x/(x^2+4) find f''(x). Please do on paper.

A:

Q: A cell phone plan charges $49.55 per month plus $14.02 in taxes, plus $0.60 per minute for calls…

A: Need to write down the piecewise function.

Q: At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg,…

A:

Q: Let a = (5,4, 2) and b = (-1, -2, -3), th 3a - 5b = (10, 2, -9). Select one: O True

A:

Q: If 1 1. f(x)dx = n(x) - tan(x) - 4² + x² + 6x + 0 4e C 3 then find f(x)

A: We can find f(x) as below, by finding the derivative.

Q: The Taylor series expansion of 2 |z| < 1 is (solve) Z-2¹ −(¹ + ² + ² + ² …..) X Option 2 O…

A:

Q: In a pool filled with water to a depth of 1 Rectangular plate calculate the fluid force on one side…

A: Given: Depth of pool = 10ft Area of rectangular plate, A = 3ft×4ft=12 ft2  Hydrostatic Force on…

Q: The United States population (in millions) is predicted to be P(t) = 317e0.01t, where t is the…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  take derivative

Q: Find a rule for the derivative of the product of four functions f,g,h, and k. Use your result from…

A:

Q: Find the radius of convergence for: 3 (n!) ³ (3n)! n=1 xn

A: Recall that the radius of convergence for a series ∑n=1∞anxn is R=limn→∞anan+1

Q: Using Rolle's theorem for the following function, find all values c in the given interval where…

A:

Q: : Use the chain rule to find the derivative of w= x² + y² with dw with x = cost + sint, y = cost-sin…

A: This question is based on chain rule differentiation.

Q: Let a = . Find a unit vector in the direction of a

A:

Q: Let ā= and b = . Find 3a + 3b.

A: Given:a→=-3,-2,3 and b→=-3,5,2We need to find 3a→+3b→.

Q: In geometric sequence the common ratio is denoted by RO

A:

Q: The Maclaurin series of the function f(x) = 2x² sin(9x) can be written as f(x) = Σcna" 71=0 where a…

A:

Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

A: We can find the area of the bounded by the given curves.

Q: an = arn+1 an = arn-1 * The general term of geometric progress Option 4 O Option 1 an=arn a" = arn-1…

A:

Q: 42. y=+on [1/2,2] 6

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to analyze and sketch a graph of the function and find any intercepts, relative extrema,…

Q: Your college newspaper, The Collegiate Times, has fixed production costs of $7000 per edition, and…

A:

Q: Evaluate the following integral. 22x² S= x4-61x² +900 Find the partial fraction decomposition of the…

A: An indefinite integral is provided. We have to evaluate it by using the partial fraction…

Q: The Eigen value of matrix p is (solve) ГО 0 Lo 1 0 0 1 -3 -4] (0,-1,-3) O (0,2,3) O (0,1,3) O…

A:

Q: Solve: y'' - 4y' + 4y = 3e ^(2x) Show all work clearly please.

A: See the details solution in below

Q: The demand function for a sofa is given by p= D(x) = 19.2 - 0.2x dollars. Find the level of…

A: We have to find level of production at which revenue will be maximum.

Q: 3. (a) Solve the differential equation (x+1) ª¹ = y +e³(x+1)² . dx (b) Form the differential…

A:

Q: The measure of the angle between the three- dimensional vectors u = (0, -1, -3) and V v = (2, 3, -1)…

A:

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: A tank contains 240 litres of fluid in which 50 grams of salt is dissolved.pure water is pumped into…

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0, 4, — 3), and R= (-6, -1, - 5)

A:

Q: B) Find the interval of convergence for the series n=0 xn √n² +3

A:

Q: Write an equation for the transformed logarithm shown below, that passes through (2,0) and (1,3) N 4…

A:

Q: Find the radius of convergence for Σ (sin²n)x". n=1

A:

Q: Use partial fractions to find the power series of the function: ∞ n=0 5æ + 53 (x − 2)(x + 5)

A:

Q: 5. Find L¹ s-1 s³ -10s² +24s

A: To find L-1s-1s3-10s2+24s.

Q: Solve the equation. dx dt 2xt² C An implicit solution in the form F(t,x) = C is =C, where C is an…

A: To find the solution of given differential equation.

Q: Convert the rectangular coordinates to polar form (√8,√8) (4,5) (√2,72) Option 4 O (2,37) (4,5)…

A:

Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: Let à . Find al.

A:

Q: Use integration to find the area between the functions y = x² and y = 3x + 4. Show your work. -4 YA…

A:

Q: (a) Find the integral of 6.x8 √21° +7 dx. **IDENTIA YAMIMATIO

A:

Q: [3 -2 21 The matrix A=0 -2 1 one of the eigen vector is (solve) Lo 0 11 250 Option 4 O [3] -2 -31 2…

A:

Q: L₁(x-3 (x-3)√x+3dx

A:

Q: The intervals on which f(x) = x² ln x is increasing and decreasing, and the intervals of concavity…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: (c) Given a cubic function i) Find the critical point(s). ENTIA ii) Hence, determine the maximum and…

A: Let's solve.

Q: Consider the following. 2(x-8)² + (y - 6)² + (z − 5)² = 10, (9, 8, 7) (a) Find an equation of the…

A:

Q: The equation (x - 1)² + (y-4)² + (z − 3)² = 25. - is an equation of the sphere with center C(1,4,-3)…

A: NOTE: Refresh your page if you can't see any equations. . the given equation of sphere is

Q: y = f(x)

A: We can answer all the three questions as below.

Q: Find all solutions of the equation 2 cos 3x The answer is x₁ = = 1 in the interval [0, π). , x₂ =…

A: The given trigonometry equation is: 2cos3x=1 To find the solution of the equation in the interval…