[Directional Derivatives] Calculate the following directional derivatives. w(x, y, z) = xy^2 / z^2 at the point (6, 1, 2) in the direction toward (5, 2, 5).

Q: ing or decreasing.

A: We have to find the following conditions according to the given information

Q: Determine whether the series is convergent or divergent by expressing s, as a telescoping sum. If it…

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Q: a) 5+3+1+(-1) ++ (-33)

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Q: 21. What's the standard form equation of a parabola with directrix x= -10 and focus (10, 0)?

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Q: -1: Determine all values of x where the following function is concave down. f(x) = 1/2x² + 1²x³ = x²…

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Q: h I 3) If you want $12,000 ten years from now, how much would you have to invest now at 15% interest…

A: Given query is to find the monthly payment.

Q: Find the slope of y = ex at x = 0.

A: Given query is to find the slope.

Q: Parameterize the plane through the point (-1, 1, -3) with the normal vector (4, 1,-2) *(s, t) = (Use…

A: To parameterize the plane through the point -1, 1, -3 with the normal vector 4, 1,-2.

Q: 7. For the parabola 4x + 2y² + 8 = 0, fine the directrix. (a) y = x = (C) 3 N|WN| W | 2 (b) (d) x =…

A: Given query is to find the directrix of the parabola.

Q: e 2x³ y = e Y

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Q: 20. Find the foci of the ellipse whose equation is given below. (x+1)² (y+3)² 36 16 -1

A: As we know the standard equation of the ellipse is: x-h2a2+y-k2b2=1 Where the center is at h,k. And…

Q: Let f(x) = {5² (52–3, 2x, x > 1, x < 1, Does lim f(x) exist? Why or why not? x 3 1. Yes because you…

A: To determine whether the given limit exists or not

Q: Determine if the limit 7 x+1 lim x-0 x -7 exists, and if it does, find its value. 1. limit = 2.…

A: We can find the limit in the below steps.

Q: Determine whether the series converges or diverges. Σ(1+1) (¹ ²0 n = converges diverges e-n

A: We can check whether the given series is convergent and divergent .

Q: y = = e(2x³+5) ²

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Q: 6. Determine lim 32. Show your work. a. -16 i b. -6 [-+x C. d. 19 119

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Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: - If cos(y) = 3 and y is in the first quadrant, find cot²/ 2

A: Given :- cosy=35, y is in first quadrant

Q: dy dx 11 1 x log x

A: ∫1xdx=lnx+cdlogxdx=1xdydx=1xlogxdy=1xlogxdxintegrate both side

Q: Determine the particular solution for the following initial value problem  dy dx = xy − 3x, y(0) = 4

A: Given differential equation:- dydx=xy-3x

Q: The US population (in millions) is predicted to be P(t)=317e^0.01t where t is the number of years…

A: Topic - Instantaneous rate of change We are given The US population (in millions) is predicted to be…

Q: 8. Let A be an n x n matrix over a field K. Show that the mapping f defined by f(X,Y)= XT AY is a…

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 2 P4(x) =…

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Q: 14) f 118 dx X A) 118x + C B) 59x-2 + C C) In 118 + C D) 118 In x + C

A: See this solution in below.

Q: Use integration by parts to find the integral. (Use C for the constant of integration.)…

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Q: Given the graph of f(x) and the labeled areas, 5 find f(x)dx S₁ 0 5 [ f(x)dx= 0 A=13 B=5 C-6 +15

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Q: Find the Maclaurin series for f(x) = cos(19x). cos(19x) = Σ n0

A: As we know that: Maclaurin series for the cosx centered at x=0 is given by f(x)=∑k=0∞(-1)kx2k(2k)!…

Q: K Find the area between f(x)=x²-7 and the x-axis from x = 0 and x = 10.

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Q: A spherical balloon is inflating with helium at a rate of 192 instant the radius is 4 ft? min How…

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Q: 26. Use the limit definition to compute f(x) if f(x) =12x²+2.

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Q: y = x², y = x

A: Here is the solution:

Q: Find the Taylor polynomial of degree n = 4 for a near the point a = π for the function cos(x). P₁(x)…

A: Solution: A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x-a)k In our case,…

Q: 1. Find the formula for the inverse function of f(x): f^(-1)(x) Express as f^(-1)(x)= f(x) = √−2x −…

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Q: Use sigma notation to write the Taylor series about x = xo for the function. cos(-5x), xo = -0.…

A: The function is given as , fx=cos-5x and x0=-π10 Write the Taylor series about x=x0.

Q: Area = [-1, "]: Consider the following solution to the problem of finding the total area bounded by…

A: Consider the following solution to the problem of finding the total area bounded by the graph of…

Q: P3 Find the Maclaurin expansion for the following functions and indicate for which values of a it…

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Q: The ellipse 13x² + 2x + y² = 1 has its center at the point (h, k) where h= k= The length of the…

A: The given equation of ellipse is 13x2+2x+y2=1 We are required to find the centre and length of major…

Q: a. Find the additional cost incurred in dollars when production is increased from 4 units to 5…

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Q: Does the infinite series O It converges. O We don't know. 10++ + 10 53/2 + converge or diverge?

A: Please see the below picture for detailed solution.

Q: 40. Toys Belkis is pulling a toy by exerting a force of 1.5 newtons on a string attached to the toy.…

A: Let a force F is applied to an object with an angle x° to the floor. Then horizontal component of…

Q: Approximate the area under the curve y = x² from x = 0 to x = 3 using a Right Endpoint approximation…

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Q: Find the average value of the function f(x)=x²-7 on [0,6]. The average value of the function…

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Q: Consider the differential equation given by: = -3y + 18 dt (A) What is the equilibrium solution? (B)…

A: Note:- These are multiple subparts question and according to company guideline we can do maximum 3…

Q: 4. Use the Fundamental Theorem of Line Integrals to calculate f Vf T ds, where C is an oriented…

A: We have to calculate the line integral.

Q: a B 2 α b Description of image (in case it has trouble loading): A right triangle has acute angles a…

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Q: 3. What is the polar equation of (a) a circle of radius a > 0 centered at the origin? (b) the…

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Q: Find the area under the graph of the function over the interval given. 26) y = ex; [-2, 8] A) e8__1…

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Q: Evaluate: ²dz dy dx Ꮭ x 4+4 O π/48 O tan-¹(2)/24 O π/96 π/24 OT

A: The given integral is: ∫02∫0x3∫0y zx4+4 dz dy dx

Q: Determine lim x--9 x²+14x+45 x+9

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Q: Which of the following sequences represents an arithmetic sequence with a common difference d = -5?…

A: Here, it is to find the arithmetic sequence with a common difference d=-5 .