Let Ƒª³ = (3z + 3x²) i+ (4y+3z+3sin(y²)) j+ (3x+3y+4e²) k (a) Find curl F. curl F= (b) What does your answer to part (a) tell you about fc F. dr where C is the circle ( – 15)² + (y — 35)² = 1 in the xy-plane, oriented clockwise? Sc F.dr = (c) If C is any closed curve, what can you say about √ F. dr? ScF.dr = -

Q: 89. A particle moves along a line so that its acceleration for r 20 is given by a(t) = velocity at…

A: The given accelaration function is

Q: Calculus I May I please have the solutions for the following questions? Thank you

A: Therefore, the required answers are a) The function is increasing in the interval (-1,1) U (1,…

Q: find the equation of the line tangent to g(x)=x^2+x at (2,6).

A: Find the equation of tangent to  at

Q: 8. Determine values of a and b so that the following function is continuous. f(x) = (2+3x-2x2 2-x…

A:

Q: The demand, D, for a new rollerball pen is given by D = 0.007p³ -0.4p² + 130p, where p is the price…

A: The demand D, for a new rollerball pen is given by D=0.007p³-0.4p²+130p,where p is the price in…

Q: Find f'(x). f(x) = 4 In (1+4x²)

A: The objective of this question is to find the derivative of the function f(x) = 4 ln(1 + 4x^2). The…

Q: How do I find all that is being asked for?

A: (a)The maximum height reached by the ball= 100 ft. (b) on the ball's way up, when it is 96 ft above…

Q: Find m and 6 such that f is differentiable everywhere. f(x) = { x² X<2 mx+b, x72

A:

Q: existence of lim

A:

Q: 6. The Apollo's Chariot, a roller coaster at Busch Gardens, moves at 110 feet per second. The…

A: Since first two questions are already solved correctly, i solve third question according to our…

Q: Find the following indefinite integrals. Ꮖ dx +C √x+6 cos(t) (6 sin(t) + 4)2 - dt = ☐ + C

A:

Q: Sketch the level curve of the function z(x, y) = y² — x² for c = 16. - 10- 9 8 7 6 5 4 3 2 + -10 -9…

A: given function

Q: Problem #9: (a) Given the initial value problem y3y 10 sint, y(0) = 9, find the Laplace transform of…

A: Answer Explanation:Step 1:Step 2: Step 3: Step 4:

Q: Suppose that f(x, y) = ex/y on the domain = {(x, y) | 0 ≤ y ≤ 1,0 ≤ x ≤ y³}. D Then the double…

A: To find:-, where

Q: 1.) The three vertices of a regular tetrahedron are located at 0(0,0,0), A(0,1,0),B(3,0), and 03. A.…

A: Given:The three vertices of a regular tetrahedron are located at ; (a)To find:the unit vector…

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: Consider the integral

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A:

Q: Find the maximum and minimum values of f(x, y) = 6x + y on the ellipse x² + 25y² = 1

A:

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

A:

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A: Domain =(-∞,∞)y-intercept is y=0x-intercepts are x=0,2There is no local maxima The local minima is…

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: Given function

Q: Graph three different non-zero vectors that sum (add up) to the zero vector.

A: We need to find 3 non zero vectors that sum to a zero vector.

Q: If possible, find the first three nonzero terms in the power series expansion for the product…

A: Solution given below Explanation:Step 1:

Q: I want to determine whether the sequence {ln(n) / ln(4n)} converges or not. When finding the limit…

A: The given sequence .The objective is to determine whether the sequence converges or diverges.

Q: A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt…

A: a) The initial concentration of the solution in the tank is 0.025kg/Lb) The amount of salt in the…

Q: Two towns A and B are 5 km and 7 km, respectively, from a railroad line. The points C and D nearest…

A: Ans : Station  s is located 2.5km away from point c.Explanation:

Q: (c) u = 2 x = a²ß, y = 32, t = √²α; u when a = -1, 3 = 2, y = 1 მ მ3 მ ди ди ди

A:

Q: Let f(x, y) = 7ln(18x² — 9y). - Graph the boundary of the domain of f below. 7- 6- 5 4- 3 2 1 27…

A: given function

Q: ds Given the velocity v= and the initial position of a body moving along a coordinate line, find the…

A: Given the velocity function    v(t) = 9.8t +6 .................(1)  and and initial position of the…

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A:

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A:

Q: ABC is a triangle with AB = 4, BC = 12, and AC 13. Find cos(A). = Note: You are being asked to find…

A: The objective of this question is to find the cosine of angle A in a triangle ABC, given the lengths…

Q: Solve y''+3y' = 6-2e3x by undetermined coefficients.

A: The general solution to the differential equation y′′+3y′=6−2e3x by the method of undetermined…

Q: Use g(x) = 1½ (x + 5)² - 1½½ to answer the following. Remember to give exact answers. (a) Solve g(x)…

A:

Q: 1. Exploration for absolute maximum and minimum. f(x,y) = x²-2xy +3y. Explore function f(x,y) on the…

A: a) The equation of the function on the border is  f(x)=2x3−2x2So, the critical points are,…

Q: Sketch the region of integration determined by the limits of integration and then switch the order…

A: InitiallyLimits areX=y/2 to X=√yAfter changing the limits of integration New limits areY=x^2  to  y=…

Q: Answer can’t be decimals, please don’t give the decimal answer

A: (a).            (2,65π​) (b).             (−2,6−π​)Explanation:Step 1: Step 2:Step 3: Step 4:

Q: Let F(x, y) = 2x 2yi + 3xyj, and C be the boundary of the square with corner points (±1, ±1),…

A: The objective of this question is to find the flux of the vector field F across the boundary C of…

Q: 7 Estimate I = 3 (2 + 3) dr using n = 4 subintervals and (a) Left endpoints. I ≈ (b) Right…

A: (a) I ≈ 13.9 (b) I ≈ 22.63Explanation:To estimate the integral ∫37​( 2/x + 3 )dx using n=4…

Q: Write the expression as the sine, cosine, or tangent of an angle. Then find the exact value of the…

A:

Q: [3] Compute the area of the surface obtained by rotating the curve, y = √√1 + 4x, 1 ≤ x ≤ 6, about…

A:

Q: Find the gradient of f, evaluate the gradient at the point P, and find the rate of change of f at P…

A: b)f(x,y,z)=xy2z3P(1,-2,1)

Q: Given = f(x, y) dxdy + f f f(x,y) dxdy, do the following. (a). Sketch the graph of the region of…

A: Given: To Find: (a) To sketch the graph of the region of integration.(b) To combine the sum into one…

Q: I am needing assitance with the problem in the attached image, 2.8.

A: Limit at x tending to -5 exist and equal to 5 . At x = -5 f(x) is not continuous.Explanation:Step 1:…

Q: Convert the following quadric surface into spherical coordinates. (x-3)^2+y^2+(z+1)^2 = 1

A: r2+2rcosΦ−6rsinΦcosΘ+9=0Explanation:Step 1:     Step 2: Step 3: Step 4:

Q: Use the figure to solve the inequality. (a) g(x)≥ f(x) (b) f(x) > g(x) (a) The solution to g(x) ≥…

A: From the graph of two functions: height of g(x) is more than height of f(x) in the interval (0,6)…

Q: Replace? with an expression that will make the equation valid 0 | dx (6x+7)=5(6x+7) ?

A:

Q: Find the inverse Laplace transform of the following: (a) X(s) (b) Y(s) 6 s²²+8s+41 360 (s+4)6

A:

Q: U-2 1.Ify= andu = x² +1, find ddy U+2 Χ at x=1. dx dx

A: The required derivative is:dxd​(dxdy​)=(x2+3)324−24x2​ The value of the derivative when x = 1 is…

Q: Given triangle ABC, the measure of angle A is 60°, the length of BC is 3, and the length of AC is 03…

A: The objective of the question is to find out the number of solutions for the measure of angle B in a…