Compute the curl of the vector field F = (x³, y³, 24). curl(F(x, y, z)) = What is the curl at the point (−3,−1, −5)? curl(F (−3,−1, −5)) =

Q: Use the midpoint rule with the given value of n to approximate the integral. 4ex dx, n=6 VE Find the…

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Q: Calculate L4 for f(x) = 22 cos (2) over [24, 27

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Q: Find the most general antiderivative for the function 8x² 4 6 x5 3

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Q: Determine the following indefinite integral. Use c to represent an arbitrary constant. (Hint: the…

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Q: Given f(x, y) = 3x²y + y3 - 3x² - 3y² + 12 (a) Determine the second-order partials: • fxx = • fyy =…

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Q: 4) f(x,y)=3e¹¹

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Q: 19-

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Q: Identify which step is incorrect in graphing g(x) = -2(x-1)4-1 Step 1: Shift right 1 unit Step 2:…

A: Given that, the function             g(x) = -2x-14 - 1

Q: (8) Find the differential for the function secr In (sina) . (A) In y (B) In y secz In (sin x) (C) y…

A: To find the derivative of y=(sinx)(sec x) we can use logarithmic differentiation as follows:…

Q: This is incorrect, also please type your answer or write clearly

A: Double integral We can solve this double integration by conversion from cartesian to polar.

Q: (7) Find the local linear approximation of f(x)=√2+3 at ro = - and use it to estimate the value of…

A: fx=12x+3

Q: If f(x) = sin (2²), which of the following is true ? (A) There is a local minimum at x = 0 (B) There…

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Q: Refer to the figure. Show that a + ß = y, and find the numerical value of tan(y). 8. a 5 A Y B 4 5

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Q: 2. Use the method of Substitution to find the following indefinite integrals

A: we have to evaluate integral ∫lnx6xdx

Q: Let f(x) = -x4-9x³+2x+8. Find the open intervals on which is concave up (down). Then determine the…

A: For a given function f( x ) ( a ) inflection points by f''( x ) = 0 ( b ) For concave up , f''( x )…

Q: Let F = (9yz)i + (10xz)j + (9xy) k. Compute the following: A. div F = 0 B. curl F = C. div curl F =…

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Q: Use finite approximations to estimate the area under the graph of the function f(x) = 24-x² + 2x…

A: area under curve is find by calculating integration of function.

Q: Find derivative of y = 2*

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Q: How did it go from step 2 to the answer?

A: The given integral is sec2(4x).

Q: (2) Graph the polynomial P(x) = x³ + x² − 5x+3 using calculus by showing the given steps: (a) Find…

A: We need to solve function and draw graph.

Q: A sample contains 560 grams of Uranium-232, a radioactive isotope, that decays according to the…

A: Given: N(t) = 560e-0.010060t  Rate when t = 20 year's

Q: Consider the polar curve r = 2 sin 30, whose graph is shown below. Set up but DO NOT EVALUATE an…

A: Given;

Q: Find the first few coefficients. Co C1 C₂ = C3 || C4 || || || The Taylor series for f(x) = e* at x =…

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Q: Question 20 Find derivative of y = x. Inx hint: use product rule In x Onone of the above O In x + 1…

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Q: Find the function's relative maxima, relative minima, and saddle points, if they exist. z = 19 x² +…

A: z=19-x2+xy-y2+21y.

Q: (-3,3)- x = 2y-y² X

A: We use Horizontal strip to evaluate the area

Q: Evaluate the following indefinite integral. Use C as your arbitary constant. £24,25 dx

A: We know that the the integral of x^n dx=x^(n+1)/(n+1)+C  Where C is an integral constant

Q: Consider the following. 5e6x = 20 (a) Complete the table to find an interval containing the solution…

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Q: Using rectangles each of whose height is given by the value of the function at the midpoint of the…

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Q: Change from rectangular to cylindrical coordinates. (Letr ≥ 0 and 0 ≤ 0 ≤ 2л.) (a) (-3, 3, 3) (b)…

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Q: Find the limit. Use l'Hospital's rule if appropriate. If there is a mo In(3x) √√3x lim x → 00

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Q: m #10: Consider the following function. g(x, y) = e5x² + 8y² + 10√√6 x (a) Find the critical point…

A: We have to find the critical points  of the  given function.

Q: The spacing on the steps are spaced a bit strangely and is a little confusing, may i get the steps…

A: we use substitution method to evaluate the integral

Q: Find the limit: lim1 [(x-1)(x+2)/(x-1)]

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Q: Sketch the graph using radians by creating a table of coordinates pairs using domains -2 π to 2 π,…

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Q: The populations P (in thousands) of a certain town in North Carolina, from 2006 through 2012 can be…

A: The population of a certain town in North carolina from 2006 to 2012 is given by:P(t)=4.2ektwhere…

Q: S √x (a) Explain why this integral is considered an improper integral. (b) Determine whether this…

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Q: A rancher wants to fence in a rectangular field and then divide it in half with a fence down the…

A: Given data Total length of fencing material is 240 feet.

Q: O f(x) dx =

A: Find integration of f(x)

Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a) (8, π/4,…

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Q: For each of the conservative vector fields below, find a potential function f. (1) F = 6yzi + 6xzj +…

A: a) To find a potential function f for the conservative vector field F = 6yzi + 6xzj + 6xyk, we need…

Q: Sketch the graph using radians by creating a table of coordinates pairs using domains -2 π to 2 π,…

A: To sketch the graph of y = cos(x) using radians, we can create a table of coordinates pairs using…

Q: 9. Evaluate each limit, if it exists, using any appropriate technique. √x + 1 1 d. lim x→0 e. lim…

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Q: Find the derivative. f'(x) = = f(x) = x sinh(x) - 9 cosh(x)

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [s sin(t)√1 + cos(t) dt

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Q: Change from rectangular to spherical coordinates. (Let p≥ 0, 0≤ 0 ≤ 2л, and 0 ≤ y ≤ π.) (a) (0,5√3,…

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Q: Find dx dy dx 11 d²y dx² x = t² + 3, y = t² + 9t = and d²y dx² For which values of t is the curve…

A: x=t2+3 , y=t2+9t

Q: The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on…

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Q: Find the exact arc length of the curve over the stated interval. y = 5x²/³, from x = 1 to x = 8…

A: We know that the arc length formula Arc length=sqrt(1+(dy/dx)^2) dx

Q: Given the differential equation y"-4y= 2e-t-6e¹t, y(0) = 0, y'(0) = -1 Apply the Laplace Transform…

A: y''-4y=2e-t-6e4ty(0)=0y'(0)=-1