Let a = (4, -2, -1) and b = (2, -2, 5). Find the projection of b onto a. proja b =<

Q: Can you simplify for the f'(x) like the instructions says

A: The derivative is: f'x=5x51x+lnx25x4

Q: Given the points A: (-6,-4,2) and B: (3,-2,0), find the vector u = AB

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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: Find the derivate of the functions: a) f(x) = -3x²³ -4 sxt9 · f'(x) = (6) g (v) = 3 2√² +5V-9 g' (v)…

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Q: Find the derivative of the function. y' = y = etan(e)

A: We use chain rule to find the derivative of the following function.  dftdθ=dfdt·dtdθ also use the…

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

A: Application of Derivative

Q: Consider the graph between two curves. Which of the following is the correct set up for the area of…

A: Consider the graph between two curves. To determine the set up of integral  that represents the area…

Q: Let f(x) = x² 50x² – 8. Calculate the derivative f'(x) = Calculate the second derivative f"(x) =…

A: Please see the below picture for detailed solution.

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: Given ƒ"(x) = 6x – 5 - and ƒ'(−2) = −1 and ƒ(−2) = 2. Find f'(x) = and find f(2)=

A: We need to find out the value of f'(x) and f(2) for which the second derivative is given.

Q: The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer…

A: We have to find m'(-1) and n'(6) Where m(x)=f(x).g(x)        n(x)=g(x)/h(x)

Q: Use double integration to find the volume of the solid bounded by the cylinder x² + y² = 9 and the…

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Q: Find the critical point of the function f(x, y) = −8+2x+4x² + 5y-y² This critical point is a:…

A: Given f( x, y ) = -8 + 2x + 4x2 + 5y - y2

Q: Complete the parametric equations of the line through the points (1,8,3) and (4,-6, (t) = 1 + 3t…

A: The parametric equation for the line through (x, y, z) and (a, b, c) is: (x, y, z)+t((a, b, c)-(x,…

Q: Each of the limits below represent a piece of the passcode that you must enter to proceed. The…

A: We have to find the limits to get the passcode.

Q: Find the surface area of revolution about the x-axis of y = 5 5 ㅠ 0 ≤ x ≤ 5 sin(5x) sin(5x) ov over…

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Q: Differentiate the function. f'(x) = f(x) = In(cos(x))

A: The solution is shown below-

Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

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Q: 400 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of pesticide at time t…

Q: Sketch-the-graphs.y = x² + 1, y = -x² + 2x + 51

A: we need to sketch the graphs of the function.

Q: 15 sin ¹√2x dx = [

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

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Q: Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the…

A: We are asked to find the  elasticity of demand

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

A: Need to find out the rate of changing of area outside the circle but inside the square changing.

Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: Given:  fx=2-62x To Find:  To determine the domain of the derivative of fx and  then to evaluate it…

Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: The given function is;  f(x)=sqrt(4-34x).

Q: Consider the graph below. Which of the following is the correct setup for the area of the shaded…

A:

Q: This was incorrect

A: The given function is; f(x,y)=ln(x3+y3).

Q: Find the derivate of the functions of at any Use the form f'(c) = lim f(x) - f (c) for a and b X->(…

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Q: Draw an accurate diagram of what follows and find resulting distance to the port: A ship sails on a…

A: We have to find, the distance from the ship to the port and the bearing of the ship from the port by…

Q: Question 18 Show that the equation has exactly one real solution. 207e+2023 In x = 7724

A: To show that the equation 207e^x + 2023 ln x = π^(24) has exactly one real solution, we can use the…

Q: Consider the following equations. y = x, y=x²

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Q: D. Name another exponential function that is equivalent to y = 2. (Hint: Recall that y = 2 * =…

A: D) The given data is: Name another exponential function that is equivalent to  y=2-x

Q: Let a = - 2ỉ - 4j – k and b = 4j + 2k. Find — ả + b. V

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Q: A volume is described as follows: 1. the base is the region bounded by x = y² + 8y + 50 and x = 2.…

A: A volume is described as follows: 1. The base is the region bounded by x=-y2+8y+50 and x=y2-22y+138.…

Q: A ball is thrown into the air and its position is given by h(t) = −4.5t² + 87t + 19 where h is the…

A: Application of Derivative

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

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Q: Find the derivative of the function. -7x³ - 6 6x² +7 f(x)=

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Q: e-1 Find the limit limä→0 tan x

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Q: Express the sequence {an} n = 1 as an equivalent sequence of the form {n}=4* n=1 {2n +5}=1 ∞ An…

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Q: Use the root test to determine convergence or divergence of the series of the series. n=1 3n¹3+n…

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Q: The integral gives the area of the region in the xy-plane. Sketch the region, label each bounding…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: We have to find the volume of the solid by rotating the region in the firs qudrant bounded by the…

Q: Let z=f(x,y) = 15x² - 25xy +9y². Find the following using the formal definition of the partial…

A: The given function is: z=f(x,y)=15x2-25xy+9y2

Q: 2y-³ Find the maximum rate of change of the function f(x, y) = X at the point (1,5)

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Q: Determine if the series O n=1 n cos (n) 3+n³ converges or diverges and choose the option that…

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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: Find the limit. lim X→0 sin (8x) 7x

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

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Q: Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

A: To Find: Tangent line to y=x3e-x, at point 1, 1e