Find f.  F"(x) = t2 - 4

Q: A ball of radius 15 has a round hole of radius 9 drilled through its center. Find the volume of the…

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Q: Name the method by determining whether I'Hôpital's Rule should be used or not. CSC x lim x+0+ √x

A: Need to write down the method to determine that l hospital is applicable or not.

Q: A video store manager observes that the number of videos sold seems to vary inversely as the price…

A: A video store manager observes that the number of videos sold seems to vary inversely as the price…

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: The number of visitors P to a website in a given week over a 1-year period is given by P(t) = 115 +…

A: Solution: Given data, P(t) = 115 +t-83e0.02t where t is the week and 1≤t≤52.…

Q: Use spherical coordinates. Evaluate III z dv, where E lies between the spheres x² + y² + z² = 4 and…

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Q: dy Find by implicit differentiation. dx x²14xy + y² = 14

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Q: Answer the following questions. 1 A function f is given by f(x) = (x+1)|x+3| x+3 (a) Express f(x)…

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Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A: To find out the critical points, increasing and decreasing intervals and also the extrema and at…

Q: The derivative of a function is given f'(z) = (2²-21-8)g(x) for some unspecified function g such…

A: The first derivative of a function is given by fx = x2-2x-8gx,   gx>0 To determine: The point…

Q: Find the derivative of the function at the given point in the direction of A. f(x,y,z)=2x-4y+7z,…

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Q: d Q10 Compute [3t²] (a) 3t² (b) 6t (c) 0 (d) 9t

A: We need to perform differentiation.

Q: Find the centroid of the triangular region cut from the third quadrant by the line x + y = -3.

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Q: Find the area enclosed by one leaf of the rose r= 10 cos (30)

A: area enclosed by one leaf of the rose r = 10 cos (3thita)   Formula :- cos2(x) = [1+cos(2x)]/2

Q: Solve the problem. 2) Given the total-revenue function R(x) = 7600x, and the total-cost function…

A: Given:- Revenue function Rx=7600xCost function Cx=x3-2x2+5x+100

Q: If is differentiable, then the function. e + f(x) √√3 is differentiable.

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Q: Find the centroid of the region cut from the first quadrant by the circle x² + y² = 81.

A: Find the centroid of the region cut from the first quadrant by the circle x2+y2=81.

Q: Find and classify the critical points of z = Local maximums: Local minimums: Saddle points: (z² -…

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Q: [1-R] [CLO 12] What is the slope of the line f⊥, where f⊥ is a line perpendicular to the line f,…

A: The given line is: 4y-3x=5

Q: Evaluate the limit sin 2x 6x lim x→0

A: N=limx→0sin2x6x∂ ∂x(sinx)=cosx∂ ∂x(xn)=nxn-1

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

A: To sketch the region bounded by the given lines. Then to express the region's  area as an iterated…

Q: (P) In(x) dx

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Q: fx cos(3x) dx

A: M=∫xcos(3x)dx∫cosxdx=sinx+c∫sinxdx=-cosx+c∫(a.b)dx=a∫bdx-∫(dadx.∫bdx)dx

Q: Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3,…

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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: Evaluate the limit sin 8x lim x 0 sin 2x

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Q: Find the volume of the solid generated by rotating about the x-axis the region bounded by y = 2.3*,…

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Q: Determine the x-intercept of the plane: [x, y, z]= [3, 1, 3]+[1, 1, -1]+[0, 1, 3]

A: Question -   Determine the X intercept of the plane

Q: A cable runs along the wall from C to P at a cost of $7 per meter, and straight from P to M at a…

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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: Q8 Find the slope at x = 2 on the graph of f(x) (a) -3 N/W (b) 3/3 (c) 3 4 = 3 (d) 0

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Q: y =(3+x)=¹/2, a = 1 Find the Linearization at a = a. L(x)=

A: To find the linearization of given function.

Q: A volume is described as follows: 1. the base is the region bounded by y = 9 - 1x² and y = 0 2.…

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

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Q: 1. Determine an equation of the line tangent to the curve y = 2x² at the point with x-coordinate-2.

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Q: Q15 Find all non-zero derivatives of the following function: f(x) = 5x³ - 7x² + 9x - 1

A: Here we differentiate f(x) with respect to x until it becomes a constant

Q: -1 If ƒ(x) is a positive 1-1 function with inverse ƒ−¹(x) with f(a) = c and ƒ(b) = d then d π ñ ["°*…

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Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A: We have to find the monotone intervals and relative extremas.

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: Determine if the function f(x) = r²-3x+2 satisfies the hypotheses of the Mean Value Theorem (MVT) on…

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Q: Sketch-the-graphs-x = 4y - y² and x = y

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Q: Evaluate cos (8x) sin-2 (8x) dx. S cos ³ (8x) sin-2 (8x) dx =

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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: 9. 87 12 5 -

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Q: Question 18 ( Show that the equation has exactly one real solution. 207e+2023 In 24

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Q: Find dy/dx at the given point without first solving for y. xy2 125 at (5, 5) d 11

A: The given equation is: xy2=125 Use the Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

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: Use calculus to find the area A of the triangle with the given vertices. (0,0) , (4,3) , (1,8)

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Q: Evaluate the limit sin 5x lim 10 sin 2x

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Q: Find the mass of the solid bounded by the planes x+z=1, x-z = -1, y = 0, and the surface y=√z. The…

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