Prove: There exist functions f, g, h in F such that g o f = h o f, but g is not equal to h.

Q: Use logarithmic differentiation to find the derivative of the function. y'(x) = y=(√x)⁹x

A: The given function is: y=x9x

Q: Find the volume of the pyramid with base in the plane z = -10 and sides formed by the three planes y…

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Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

A: f(x,y)=5-4x+6y-3x2y∂ ∂x(xn)=nxn-1∂ ∂x(constnat)=0

Q: y" + 3y + 2y = 4x² 3 e² y (0) = 9, y' (0) = 5

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliary…

Q: A solid is constructed so that one side is the region between the lines x = a, x=b, the graph of y =…

A: The given data is:   y=fxx=ax=b

Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. 6 X₁ = 1, X₂…

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Q: Find the distance from the point (7,-4,5) to the line a(t) = (5,-3, -2)t + (6, 8,-4). Calculator

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Q: Evaluate the triple integral. JJL. TV₂ where G is the solid in the first octant that is bounded by…

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Q: differential equation dy/dx= 2^-x at the indicated point

A: Given  y'=2-x x y' 0 1 1 0.5 -1 2 2 4 -2 4 3 0.125 -3 8

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: Given: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then…

Q: J xlnxdx X X

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Q: Sketch the graph that possesses the characteristics listed. f is concave down at (1,5), concave up…

A: We need to find the graph which have the following characteristics f is concave down at point (1,5)…

Q: 113 Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: 4. CO Σ n=0 3 4+1 51-n

A: The series is given by ∑n=0∞34n+151-n To evaluate: The value of series.

Q: Question 17 () Let / be defined as follows: {² z Using the definition of the derivative, compute…

A: Let f be defined as follows:  fx=x2 if x<0x if x≥0 By using the definition of derivative, to…

Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A: If x=c is a critical point of the function f(x) if f(c) exists and if either f'(c) =0 or f'(c) does…

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: A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material…

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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 rectangle has its base on the x-axis and its upper two vertices on the parabola y = 25 - x². What…

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Q: The weight of a fish varies jointly as its girth and the square of its length. One fish weighed in…

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Q: Use linear approximation to approximate √81.2 as follows. Let f(x) √. The equation of the tangent…

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Q: The figure shows a lamina that is shaded according to the given density function: darker shading…

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

Q: 3) Curve Sketching: The function y = f(x) and its derivatives are given below. Use the information…

A: We have to plot function using given information

Q: S Du Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3r sin(ry)…

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: Q18 Given s = 3a²c-2bc + 5abc² (a) (b) da dc || ||

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Q: A tepee has a circular floor with a diameter of 4 meters. What is the floor's circumference? typed…

A: Given :  A tepee has a circular floor with a diameter of 4 meters. Find :  What is the floor's…

Q: Find the surface area of revolution about the 2x + 2 over the interval x-axis of y 1 < x < 4.

A: y=2x+2, 1≤x≤4 Differentiating with respect to x, we get dydx=21+0=2

Q: ƒ (x) = (x8 – 2x) g(x) = (x² + 6x h(x) = 2x - 11 m(x) = f(x) g(x) n (x) g(x) h(x) m' (-1) = n' (6)=…

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Q: Find the volume of a pyramid with height 29 and rectangular base with dimensions 3 and 8 using…

A: Let h be the height of the pyramid, and l and w be the length and width of the pyramid. Note that,…

Q: The position of an object with respect to time is given by the following function: d(t) = d³ +21² -…

A: Given poistion function:- dt=d3+2t2-2

Q: a) Suppose that lim n-00 ∞ The series Enan n=1 an+1 an 1 == 2 converges ✓ by the ratio test <

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Q: Find lim f(x) if, for all x > 1, x → 00 4 12ex - 24 4ex X 3√x √x-1

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Q: Find the limit. lim 0-0 cos(0) 1 sin (0)

A: Given limit limθ→0cosθ - 1sinθ

Q: A rectangular tank that is 2048 ft³ with a square base and open top is to be constructed of sheet…

A: The given data is: A rectangular tank that is 2048 ft3  Base is square Find the dimension of the…

Q: A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 90 ft high. a) How…

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Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 4y and y³ = x with y…

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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: п Convert the point (p, 0, 0)=(3, 377) 6 expressions, or decimals to at least one decimal place. (x,…

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Q: A simplex matrix is given. 1 10 X = 01 y = 4 5 7 12 12 0 9 0 14 00 The solution is complete, so…

A: We have to find the maximum value of f and values of x,y.

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

A: Given function is:fx=-0.001x2+4.2x-80We have to find the absolute extrema of the function.

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

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

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Q: the answer is incorrect

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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: In evaluating 2₁3² (x³ − 1) dx, we make the substitution u O O x³-1 dx (x³ − 1) 3x²

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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,…