Find the directional derivative of f(x, y, z) = z³ — x²y at the point (-5, 4, -2) in the direction of the vector v = (1,5, −5).

Q: Sketch the region enclosed by the curves x = sin 5y and x = 10 A = and compute its area as an…

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Q: 1. Evaluate the area bounded by the parabola y2 = -2x + 5 and the line x + y + 5 = 0.

A: To evaluate the area bounded by the parabola  and the line .

Q: If a function h satisfies h(-x) = h(x) for every number x in its domain, then h is called an even…

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Q: Find the domain of the function g(x) = x³ + 11x - 2 X - 3|- |x+1|

A: To find the domain of the following function.

Q: Fill in the blank with the correct choice. Suppose f(x) is decreasing over the interval [7, 13], and…

A: If a function f(x) decreases over an interval [a,b], which means..

Q: Find the derivative for the function f(x)=√x³

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Q: Suppose a product's revenue function is given by R(q) = -3q2 + 200g, where R(q) is in dollars and q…

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Q: Evaluate 28 - 19 the definite integral d x

A: Evaluate the definite integralI=∫−1928dx

Q: For the relation x²y - y² = 1 - x, find its first derivative at the point where x = 1 and y = 0.…

A: For the relation , to find its first derivative at the point where  .

Q: The population of rabbits in a certain region without any predators t years from now is given by the…

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Q: Calculate the value of a that will make the function below continuous. Answer: 0 TO If it is not an…

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Q: 9 Find the linearization of f(x) = x at a = 8. Use it to approximate 8.1 (Show your work)

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Q: Producers' Surplus The manufacturer of a brand of mattresses will make x hundred units available in…

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Q: For the following demand function, find a. E, and b. the values of q (if any) at which total revenue…

A: Solution

Q: Let the line PQ pass through the points P = (10,-2, 1) and Q = (11,6,8). The line will pass through…

A: Given Two points

Q: n=1 n (-1)" 4n+2

A: The given series is

Q: f (x) = = Enter your answer by filling in the boxes. x - 7x-6 f(x) = ( D)(C D)([

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Q: REMARK: You will be asked to submit your work for this question at the bottom of this assessment. dy…

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Q: 13 12 /(1-11) de- =

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Q: Jse Green's Theorem to evaluate • f F - dř, where F(x, y) = ( −6xy, y³ − 3) and C is the rectangle…

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Q: Identify the function's local and absolute extreme values, if any, saying where they occur. f(x) =…

A: The given function is .The objective is to find the local extremum of the given function.

Q: = Find the first 10 terms of the sequence an Its 9th term is Its 10th term is 1 an-1 and a₁ = 23.

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Q: Complete the following steps for the given function, interval, and value of n. a. Sketch the graph…

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 9 - x, y…

A: Given function

Q: O Find the derivative for the function f(x): = 5 x

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Q: (ii) [√x sin(1 + x³)dr. (iii) Choose a suitable u-substitution to prove that far sin √ dr. reduces…

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Q: Find the area of the region. two petals of r = 10 sin(30)

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Q: Decide whether each step in the solution below for solving the system of two equations in two…

A: The given system of equations is

Q: At what point does the curve have maxium curvature? y=5ex (x,y)=(___) What happens to the…

A: To find the point where the curve y=5ex has maximum curvature, we need to calculate the curvature…

Q: Find the radius and interval of convergence of the ff power series B (x-2)^ 2n-1 ^=U 2

A: The power series:Using the ration test:

Q: 2πT Find all solutions to cos(80) — cos(20) = sin(50) on 0 ≤0< 3 0=3,782,3,11 18 Give your answers…

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Q: Estimate the limit numerically or state that the limit does not exist. lim 2-0 9² - 1 I

A: limx→09x−1xf(x)=9x−1x

Q: S SS z d E with vertices (0,0,0), (3,0,0), (0,6,0), and (0,0,2) Find z dV, where E is the solid…

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Q: Find the derivative. ƒ(x) = (7xº + 7)³ 5 (7x6+7)°. (42x7 + 7x) 210x5 (7x6 +7) ¹ 4 4 05 (7x6+7) ¹ 5…

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Q: please help solve, Use a triple integral to find the volume of the tetrahedron bounded by the planes…

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Q: Find the following volumes using cylindrical shells: The region bounded by the curve y = cos(x²) and…

A: Solution is given below.

Q: The function shown on the graph above, has the formula f(x) = Prove algebraically or numerically…

A: We need to prove that there is a hole at x=0.

Q: The position of an object moving along a straight line is given by the equation s = t³9t² + 15t +4…

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Q: IF f(x) = 13sin(x)-8e*. Calculate: df(x) dx =

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Q: Given the function: m(y) = -√ Calculate: dm(y)_ dy

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Q: Q(t) = What amount (in grams) will be left after 25.3 days? (Round your answer to three decimal…

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Q: For the following indefinite integral, find the pull and then give Power series centered at x = 0…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. A1 y=f(x) A2 5 A/ A3…

A: Graph of the function is givenWe have to find .

Q: Write the augmented matrix for the following system of equations in the table below. You'll have to…

A: Write the augmented matrix for the following system of equations.u+v+2w=12v−5w=23u+5v+w=1

Q: 1 The line / is tangent to the curve y=1-- , where x0, at the point where x = a. Show that the…

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Q: Charging the Capacitor Having stabilized the fuel, you look to your computer for next steps. You are…

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Q: Given the vector function r(t) = (-t, -4t³, -3t¹ +5) Find the velocity and acceleration vectors at t…

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Q: Let r(t) = [F(t)dt (don't include the +C) Find

A: The position vector is given byTo determine: The value of .

Q: Find the volume of the region bounded above by the paraboloid z=4x² + y² and below by the square…

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Q: Find a parametric representation for the surface. the part of the ellipsoid  x2 + 7y2 + 5z2 = 1 that…

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