Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

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Q: Use linear approximation, i.e. the tangent line, to approximate √16.2 as follows: Let f(x)=√x. Find…

A: Given: f(x)=x at x=16

Q: ind the derivative of the function. y = e-7x In(4x)

A: y=e-7xln4xd dx(lnx)=1xd dx(ex)=exd dx(a.b)=adbdx+bdadx

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A: Derivative

Q: Consider the function f(x) = 12x³ +30x¹ - 160x³ +4. f(x) has inflection points at (reading from left…

A: Application of Derivative

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A: Given: Crown length (in mm) of the molar t weeks after conception L(t)=-.015t2+1.38t-7.1 To find:…

Q: Determine the average rate of change of the function over the domain graphed. (-3,5). y (3,5) 41 2…

A: From the given graph  of the function f(x)   The function is defined for the interval [-3,3]   To…

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Q: 1. Find the limit limä→∞ (1 + 3 X 5x

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Q: If f(7) = 7 and f'(7) = 4, estimate f(6.7). f(6.7)~

A: f(7)=7f'(7)=4from leanear approximation f(x)=f(a)+f'(a)(x-a)

Q: Find the future value of the following ordinary annuity. Payments are made and interest is…

A: Given : Find the future value of the following ordinary annuity. Payments are made and interest is…

Q: Instagram has a revenue function of R(q) = 5q 2 − 10q+ 600 and a cost function of C(q) = 3q 2 + 200,…

A: Note: As per our guidelines, we are supposed to answer only one question with a maximum of three…

Q: 4 Function f is defined by f(x)= √√x+1, -1<x<1 x-1, otherwise (a) Find lim f(x), lim f(x), lim f(x)…

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Q: Find the derivate of the function F(x) = x²(x²-8) a) C 2 6b) f(x) = (5x²³²-7) (6x + 1) F'(x) = c) 5…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

A: We need to change the integral into polar integral ∫0ln6∫0ln62-y2ex2+y2dxdy

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Q: 5. Find the explicit solution of the given initial-value problem. dy e-x-ex dx 3+4y a) = y(0)=1 (b)…

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Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

A: given  x2+y2=136d dx(xn)=nxn-1d dx(constant)=0

Q: ts) Let f(x) = 1. f'(x)= 2. f'(4)= 5x² tan(r) sec(x) Find the following:

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Q: Find the inflection point for the function shown below. If there are more than one, be sure to…

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Q: Using the ratio test to determine the convergence or divergence of the series series. O Convergent…

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Q: TOPIC 4-5: L'Hôpital's Rule x²-25 x+∞5-4x-x² Q. #11 Please evaluate Lim a) Using L'Hôpital's Rule as…

A: L’hospital rule  limx— a f(x)/g(x)   = limx— a f’(x)/g’(x)   now find limit

Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

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Q: The perimeter of a rhombus is 68 inches and one of its diagonals measures 30 inches. Find the area…

A: Topic = Geometry

Q: Determine the PDE of all surfaces cutting the family of cones given by x²+y²-a²z²=0

A: The family of cones given by the equation:   x^2 + y^2 - a^2*z^2 = 0

Q: The region bounded by f(x) = −3x² + 12x + 63, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: Some value of f(x) and f'(x) are given in the table. If no value is given, then you should assume…

A: Given Table:- x 4 5 6 f(x)   -3   f'(x) 1 ϕ 1

Q: Consider the function f(x) = 12x5 +75x¹ - 120x³ +1. For this function there are four important…

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Q: Use logarithmic differentiation to find the derivative of the function. y'(x) = X-3 x + 3

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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: Cost, revenue, and profit are in dollars and x is the number of units. The average cost of a product…

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Q: Suppose that f (x, y) = xy. The directional derivative of f(x, y) in the directional (1,-4) and at…

A: Given: f(x,y)=xy To Find: Directional derivative at point (4,-1) in the direction &lt;1,-4&gt;

Q: Expand the quotient by partial fractions. 6x - 10 x - 4x +3 6x - 10 2 x - 4x +3 (Simplify your…

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Q: Find all the complex roots. Write the answer in exponential form. The complex cube roots of 16+16i

A: Given:  z = 16 + 16i

Q: what is the general solution to 2x^(2)y''+5xy'+y=0 what is the particular solution to…

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Q: Find the absolute maximum and minimum values of the following function over the indicated interval,…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Find the linear approximation to the equation f(x, y) = 3₁1/ approximate f(4.14, 2.19) xy at the…

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the 7+x…

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Q: Consider the function ƒ(x) = x¹ − 18x² +8, −2 ≤x≤7. This function has an absolute minimum value…

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Q: An object traveling in a straight line travels s(t) kilometers after t hours, where s(t) = t² + 3t.…

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Q: 2√3/3 3/2 21 7(²-1) ³92 - -dr = r (Type an exact answer in terms of .)

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Q: Change the Cartesian integral - ² dy dx into an equivalent polar integral. Then evaluate the polar…

A: To change the Cartesian integral ∫-55∫025-x2 dy dx into an equivalent polar integral. Then to…

Q: Find a) any critical values and b) any relative extrema. 3 g(x)= = -x + 3x-6 a) Select the correct…

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Q: 3x³+1 f) lim x →∞0 4x³-1

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Q: Find the derivative of the function. f(0) = cos(0²) f'(0) = =

A: Given   f(thita) = Cos(thita2)

Q: Consider the function f(x) = 1−3x², -3 ≤ x ≤ 1. Use the derivatives to algebraically answer the…

A: Given, As per given question we need to find the extreme points of the function fx=1-3x2 on the…

Q: Evaluate the limit using L'Hospital's rule if necessary lim (1 + 4) * I→∞

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Q: V 5 4 3 2 1 -1 -2 -3 -4 The graph above shows the base of an object. Compute the value of the volume…

A: Given figure:-

Q: Consider the curve 1x² - 4xy – 2y³ = 290.25. (a) Find an expression for y'. y' = = (b) P(-13.5, 3)…

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