Find the divergence of the vector field F = < yx², xy³ > div F = Calculator Check Answer

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Q: The length, width w, and height h of a box change with time. At a certain instant the dimensions are…

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Q: A company charting its profits notices that the relationship between the number of units sold, x,…

A: A company charting its profits notices that the relationship between the number  of units sold, x,…

Q: Consider the following vector field. √x 4 + Z F(x, y, z) = i + √y 4 + X (a) Find the curl of the…

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Q: Evaluate • Sf. dr. 1 F(x, y) = xi + yj C: r(t) = (5t + 1)i + tj, X 0 st≤ 1

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Q: The surface of the dome on a new museum is given by r(u, v) = 16 sin(u) cos(v)i + 16 sin(u) sin(v)j…

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Q: f(x) = 2000 + 500 In (x), x>1 For the N(x) given above, find f'(10) 500 O 50 O 2050 2500

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Q: Find the directional derivative of the function f(x, y) = ln (x + y³) at the point (-3,2) in the…

A: The given function is:f(x, y)=lnx2+y2Given point is:  P=(-3, 2)Direction vector is:  v→=-2, -3

Q: A fluid has density 1000 kg/m³ and flows with velocity = a + y + zk, where x, y, and z are measured…

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Q: Find the divergence of the vector field F = div F =

A: given, F¯=&lt;3zcos(x),5zsin(x),7z&gt;

Q: Evaluate the line integral, where C is the given curve. √xyev² dy, C: x = 2t₁ y = 3t², z=2t³, ostsi

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Q: Find the curl of the vector field F = curl F - Calculator Check Answer (5y cos(x), 2x sin(y)) k

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Q: many different 8-digit phone numbers do not contain the digit 4? Assume that any digit in the phone…

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Q: What is the general formula for the th term of the sequence-4, 1, 8, 17, 28,...

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Q: x-f(x) 2x + 3 Find k'(-2), given that Let k(x)= Provide your answer below: K'(-2)= f(-2) = -3,…

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Q: Find increasing interval for f(x) = x² - 4x +9 O none of these answers O (-infinity, 2) O (1,…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the specified…

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Q: f(0) = {! 0 2≤1≤3 otherwise. Find the Laplace transform F(s) by computing the following integ 1.…

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Q: Find the equation of the line passing through the points (-8,-1) and (-8,-7)

A: The given two points are (-8,-1) and (-8,-7), we have to find the equation of line passing through…

Q: Find the indefinite integral. x6 - 2x dx X 6 •x-2x st st -dx =

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Q: (a) Find the differential dy of y = tan 3x. (b) Evaluate dy for x 3π/4, dx = 0.3. dx (a) dy = = (b)…

A: a) y= tan(3x) dy/dx = d/dx(tan3x) dy/dx= 3sec2x(3x) dy= 3sec2(3x)dx

Q: Find the inverse of the matrix. 3 13-1 -22 2 1

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Q: Solve for x (here log = log10): A B x = 10 x = 50 C x = 100 D x = 500 log(x) log(5) = 2

A: The given logarithmic equation logx-log5=2. We have to solve the value of x.

Q: (n+5)(x−4)" 17" 3)f(x) = Σ What is the radius of convergence? What n=0 is the interval of…

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Q: Consider the following. 8 [³17 1/ X /1 17 In(x) dx

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Q: For angle \theta in the first quadrant, sin\theta =(2)/(3). What is the value of cot\theta ?

A: Sin(θ)=(2)/(3) θ is in first quadrant  We have to find cot(θ)

Q: Graph the exponential function. -(-)* Plot five points on the graph of the function. Then click on…

A: An exponential function,

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(9, 3,…

A: We have to show if the given points are of parallelogram and find its area. For this firs we will…

Q: 1) a) Find the exact length of the curve y = X 1 + 6 2x y = b) Find the exact area of the surface…

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Q: Determine whether the series converges or diverges. n = 1 converges Odiverges Vi+n 3+n

A: To calculate the convergence and divergence of the series

Q: Set up the definite integral that gives the area of the region. Y₁ = (x - 1)³ Y1 1 S Y₂ = x - 1 Y2…

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Q: d √(x8+2x³+7) dx = 6 dx

A: We know that the integral of x^ndx=x^(n+1)/(n+1)+C  And derivative of x^n=nx^(n-1)

Q: What is the formula for each step of Euler's method, for the differential equation Dy/dx=f(x,y)

A: Euler's method is a numerical method for approximating the solution of a first-order ordinary…

Q: Let f(x)=√x. (a) Use linear approximation at x = = 125 to approximate f(124.7) = 124.7. The Linear…

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Q: The area under the curve is also the ________________ of data between any two points.

A: The area under the curve is also the ________________ of data between any two points.

Q: 3. Use the properties of determinants (not the co-factor expansion) to show that 1 x x² 1 y y²…

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Q: can you please annotate this and show all working out

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: ¾√/1-2x³²-7X F(x) = x²³ Find The F(X)

A: Differentiation By using chain rule we can solve this given function derivative.

Q: (6) Given the function f(x) (4) (-2) = = 1 x +3 and g(x) = x², find: (fog)(x) = (gog)(x) =

A: Given f(x)=1x+3  and g(x)=x2, we need to find:

Q: Differentiate in two ways: y = (x + ¹)(x - ² + 1)

A: We know that the product rules of the derivative d/dx(uv)=u*(dv)/(dx)+v*(du)/(dx)

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: The given curve x=t and y=t2-2t. We have to find the equation of the tangent line at the point t=9.

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (10, 12, -2) (60,24,156)

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Q: Find Suppose z and y are implicitly related by the equation sin (3x - y) = zy +11 for a general…

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Q: End a f4 4x cos (11 - 5x²) dx. Simplify your answer. Answer:

A: ∫ 4x· cos11-5x2dx

Q: Which numerical method is more accurate, the Euler method or the Runge-Kutta method?

A: Here we have to tell which method is more accurate when compare to Euler method and the Runge-Kutta…

Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

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Q: Use the graph below to fill in the missing values. -1 2 + f(0) f(x)=0 x = f(0) = f-¹(x)=0x=

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Q: Use a line integral to find the area of the region R. R: triangle bounded by the graphs of x = 0, 5x…

A: Given, the region R is bounded by x=0,5x-2y=0, and x+2y=12.

Q: What is the minimum order of the Taylor polynomial centered at 0 for cos x required to approximate…

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Q: A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out…

A: area of cardboard=A×B=143 in2height of the box, h=2 in