Integral Calculus Applications Suppose we have marginal revenue (MR) and marginal cost (MC) functions:  MR (q) = 8 - 6q + 2q2 MC (q) = 2 + 60q - q2 Determine Intervals where utility function is increasing and decreasing.

Q: if 1+1=2 and 1-2p 1+3p If 2 are the probabilities of three 4 mutually exclusive events, then find…

A: Given that The Probabilities are 1+3p3, 1-p4, 1-2p2 Since 1+3p3, 1-p4, 1-2p2 are mutually exclusive…

Q: Calculate the below contour integral. (Hint: Use Cauchey's integration formula) $ |z|=2 dz z³(z + 4)

A:

Q: Use the rules for multiplication and/or division of measurements to evaluate. (Round your answer to…

A: Note that, (120 V²)35.9 ohm=120×120 V²35.9 ohm=14400 V²35.9 ohm= 401.11 watts

Q: [7-3] 6 . For each eigenvalue of B, find a corresponding eigenvector. . Find the eigenvalues of B =…

A: Eigen value can be found by using determinant of Matrix - (Lembda)(I)= 0

Q: Minimize function using dual simplex method Objective function:w=8x, +4x₂+6x3 Constraints: 3x₁ + 2x₂…

A: We know that if the optimal value of the linear programming problem exists then, the optimal value…

Q: 9. Use any test to determine whether = the test you use. 5n+3 2n² +6n-1 converges or diverges and…

A:

Q: 6. Give a formal proof demonstrating that ¬(pv q) is a logical consequence of p

A:

Q: 5 i. Sine ii. Cosine iii. Tangent iv. Cosecant v. Secant vi. Cotangent b. Find the value for Ⓒ

A:

Q: Q17. Suppose M is a stochastic matrix representing the probabilities of transitions each month.…

A:

Q: DOOR 6504 I 1818 8 DOOR_ 2138 - 188 00 9 DOOR. 5)290 8

A:

Q: Use intermediate value theorem to prove that a cubic  x3+ax2+bx+c=0 for at least one real value of…

A: Intermediate value theorem: If f is function which is continuous at every point of the interval…

Q: d(x,y) Solve the system u = x-y, v= 3x + 3y for x and y in terms of u and v. Then find the value of…

A: Jacobian is defined as considering x and y to be two functions with respect to two independent…

Q: 3. The trigonometric equation cos²x- sin²x = 0 has the same solutions as the trigonometric equation…

A: In the given problem we have to show that two trigonometric equation has the same -solution.  If we…

Q: # 75 Find y'(7/2) - e-¹-74 if y solves the initial value problem y + sin(2t)y = sin(2t), H y(0) = 1,…

A:

Q: Evaluate the line integral Vp dr for the following function and oriented curve C (a) using a…

A: Evaluate of parametic line Integrals

Q: OAD BC ☐AC CD U Find the minimum cost spanning tree on the graph above using Kruskal's algorithm.…

A:

Q: Use the shell method to find the volume generated by revolving the shaded region about the y-axis.…

A:

Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n'=dxn, b' = d x b and…

A:

Q: In constructing an open rectangular box from 108 ft of material, what dimensions will result in a…

A:

Q: Evaluate the following integral. √xº In (7x5) dx

A: Evaluation of integral by integral by parts

Q: 3) Find the natural cubic spline for the following values: xy -15 10 47 Show all your steps.

A:

Q: Evaluate S (x + y)dxdy, where R is the trapezoidal domain with vertices given by (0,0), (5,0), (5/2,…

A:

Q: Consider the differential equation (2xy + 2x + sin x) dx + (x²- - cos y) dy = 0 (a) Is the equation…

A:

Q: A model for the population, P, of dinoflagellates in a flask of water is governed by the ordinary…

A:

Q: 9. Clearly explain, using correct mathematical terminology, the difference(s) between the graph of y…

A:

Q: Let X be a normed space, z = X and f = X'. Show that T: X → X defined by T(x) = f(x)z, XE X is…

A:

Q: Let w = f(x, y, z). The expression fi (x, y, z) Ax + f2 (x, y, z) Ay + ƒ3 (x, y, z) Az is c O the…

A: Answer : Option (c) is correct.

Q: c) Use an implicit description to find the area of the surface 2x3/2+2y³/2-3z = 0 above the square R…

A: Since multiple questions have been posted, we have solved the first question for you, please post…

Q: Let A = {1,2,3}, Define the functions f: A → C and g: B → C by f(1) = 7, f(2) = 9, f(3) = 7, g(4) =…

A:

Q: If complex numbers z₁, 22 and 23 are such that |z₁| = |22| = |23|₂ (3)- then prove that arg = arg Z2…

A: The given problem is to prove that for the given complex numbers z1,z2,z3 and |z1|=|z2|=|z3| to…

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

A:

Q: Which scenario could represent the expression 2 = ? O A biker lives 23 miles from her friend's…

A:

Q: STATE OF Economy           PROBABILITY        RATE OF RETURN IF STATE  OCCUR   --------------------…

A: Given: The information in the form of a table regarding the state of the economy and its probability…

Q: Given [a b C d g A e h = 40 and B fi Lc ra + A d g b + B _c + C e f 4- h = ? i] d g e h = 50 f i

A:

Q: (d) f(x) = cos(x) (e) f(x) = x² sin(x)

A: The given problem is to find the maclaurin series of the given functions f(x)=cos(πx) and…

Q: Evaluate the surface integral surfaces, use the positive (outward) orientation. Js F. ds for the…

A:

Q: 32. Which has a greater magnitude: owing $42 or earning $12? 112

A:

Q: Find the general solution of the recursive relation an = 2an-1-12an-2 for every integer n > 1. None…

A:

Q: Q18. Suppose M is a stochastic matrix representing the probabilities of transitions each day.…

A:

Q: (a) (b) With usual notations, prove that : T +""] = [~" ** -**] =k³ [kt'-k't] =k³ d ( = } ds k…

A:

Q: Q4: Sketch the phase plane portrait of equation (without explicitly computing its solutions),…

A: As per the question we are given a dynamic system governed by the following 2nd order linear…

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (0,5,3) S…

A:

Q: Express the definite integral as the limit of Riemann sums on the given interval using right-hand…

A: The definite integral of a continuous function f over the interval a, b, denoted by ∫abf(x)dx, is…

Q: Find the first five non-zero terms of the Taylor series for f(x) M8 + Written compactly, this series…

A:

Q: Given that 0. M8 n=0 x = 1 1- x to x = = Identify its interval of convergence. The series is…

A:

Q: a. Find the normal vector to the tangent plane b. Find an equation of the tangent plane to the given…

A: To find normal vector to any curve at any point we need to find it's gradient, also equation of…

Q: Find the maximum value that f(x, y, z) = x² +9y - z² can have on the line of intersection of the…

A:

Q: Use the alternating series test or the test for divergence to determine whether converges or…

A: Given series is  ∑n=1∞-1n(5n+4)3n2-2 (.) Alternating series test :…

Q: Find the flux of the vector field F= (0,0,3) across the slanted face of the tetrahedron z = 2-x-y in…

A: