1. Find the point (s) at which the following parametric curve x = t², = t³ - 9t intersects itself. Find the equation of the tangent lines at these po Y

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

A: Solution: Given data, h = 15t - 1.86t2   a) velocity = h' (t)   → h' (t) = 15 - 3.72t   t=3 h(3) =…

Q: The demand for a new computer game can be modeled by p(x) = 55-4 Inx, for 0≤x≤800, where p(x) is the…

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Q: 5. Find the points of inflection and discuss the concavity of the function (x)=-8x-2 cos x on the…

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Q: A bookstore sells 96 history textbooks per month at $120 each. The owners estimate that for each $10…

A: let number of $10 price increase is x

Q: Determine whether the function f has a derivative at c. If it does, what is f'(c)? (If an answer…

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Q: At what point on the curve  y = 8 + 2ex − 4x  is the tangent line parallel to the line  4x − y =…

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Q: Find the derivative of f (y) = 9 tan (y) - Enclose arguments of functions, example, sin (2x) or…

A: to find derivatives

Q: y 2 y = f'(x) 4 6 x

A: here , we have graph of the derivative of function  f means  f' :-then finding following :-(a)…

Q: The position function of a particle is given by r(t) = (4t², (4t², 5t, t²- 1t). 1 At what time is…

A: rt=4t2, 5t, t2-1t To find the velocity, differentiate the position function with respect to t, we…

Q: Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and…

A: since it is given that, Sodium chlorate crystals are easy to grow in the shape of cubes by allowing…

Q: If f(t) = (t² + 6t+4) (2t² + 2), find f'(t). Find f'(3). Question Help: Video Message instructor…

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Q: Let be a quadrant II angle with sin(0) = = Find sin 0 2 √89 10

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Q: True or False: The expression x + 5 is a factor of x4 + 3x³ - 42x² - 6x +80. A B True False

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Q: Itranscript a. Determine whether the Mean Value Theorem applies to the function f(x) = In 16x on the…

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Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…

A: Given: Mx,y,z=12x-y2+xz+240The radius of the spherical planet is 12 unit. Hence, x2 + y2 + z2 =…

Q: X(35X [En(x) ? dx

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Q: Solve the given differential equation. 3ydx - 3xdy + x* dx = 8dx The solution is (Type an equation.)

A: Given differential equation 3ydx - 3xdy + x4dx = 8dx

Q: Use matrix inversion to solve each collection of systems of linear equations. HINT [See Example 4.)…

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Q: Evaluate SSSW f(x,y,z) dV for the function f and region W specified: f(x,y,z)=24(x+y) W:…

A: triple integral

Q: Volume = --1 1,0

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Q: Which of the following conditions form the HYPOTHESIS for the basic form of L'Hopital's Rule? Let f…

A: Use the concept of L’Hopital’s rule when determining a limit.

Q: 15. Evaluate the limit for the graph: lim f(x). *→2* 4 +∞o a. b. -1 14 A 2 -2 0 2 A C. d. 2 does not…

A: Solution:

Q: Is the integral convergent or divergent and if convergent evaluate the integral.

A: Given :

Q: Match each of the trigonometric expressions below with the equivalent non-trigonometric function…

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

Q: How many inflection points does  Which points are inflection points? (List the labels of the points…

A: To find inflection points of the given graph

Q: still can't understand. please provide more info

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Q: 2. a) Estimate the instantaneous rate of change of the function at the tangent point (7,9) indicated…

A: Given,

Q: 5. Consider the region R bounded by y=1-x² x = 0 and y = 0 [This region is used to answer questions…

A: Draw the graph and then select the region.Take a small volume of a cross section area and integrate…

Q: Evaluate the integral. 9 y4 SS 4 y 3 y X dxdy

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Q: 700 (p+1)³² For the demand function q = D(p) = a) The elasticity b) The elasticity at p = 1, stating…

A: The demand function is given as , q=Dp=700p+13

Q: 3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any…

A: Solution: (a) If (x,y) approaches (0,0) along the straight line y = mx, then we can substitute mx…

Q: 1. Find the linearization of f(x) = (x³ + 1)¹/² at x = 2 and use this to estimate f(2.05).

A: Please see the below picture for detailed solution.

Q: For each number line problem below, identify the computation it models. (Select all that apply.) (а)…

A: To Find : Computation it models through given figure

Q: Find dy dx using implicit differentiation. A 6x² +9y 8x +9y² Hint: First clear the denominator to…

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Q: Suppose that f(x) . (If an answer does not exist, enter DNE.) (a) Find all partition numbers of…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. kindly repost…

Q: 2. Let D be an open, connected but not simply-connected subset of R2. Give an example of vector…

A: The answer provided below has been developed in a clear step by step manner

Q: Find the volume of the solid obtained by rotating the region bounded by the curves: y = 2x, y = 4√;…

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Q: Differentiate the function f. f(x)=-3x - 5 F'(x) = Graph y = f(x) and y = f'(x) on the same set of…

A: Given : differentiate

Q: - y² = 4 in the first quadrant.

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Q: Evaluate the limit for the graph: lim f(x). X+2+ O -4 +00 0-1 01 -00 4 2 -20 -2 24 4 8

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Q: : )₂² dx = 2M²+1 Jam x m+1 +( Connected to AmerEast-1. [ 2/²3 - 42²2 + 92]," 니 | [213 - 4 ( 22² +9…

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Q: The equation A(t) = 2000e0.045t gives the balance after t years of an initial investment of 2000…

A: Equation given A(t) = 2000e0.045t Find - (1)  dA/dt(2) Find and intepret A'(5)(3)  compare the…

Q: Evaluate the integral by interpreting it in terms of areas. 6² ( 1² x - 2) αx -X dx

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Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 2, assuming that a(2) =…

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Q: A ball is thrown upward. Its height hin feet is given by h(t) = 104t - 16t², where t is the time…

A: Given height:- ht=104t-16t2

Q: Solve the given differential equation. ex² dy=x√/9-ydx Choose the correct answer below. =9-²+C 4 ○…

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Q: 2) f(0) = f(2)=0 f'(x)>0 on (-∞,1) ƒ'(1) = 0 f'(x) <0 on (1,0) ƒ"(x) <0 on (-∞,∞)

A: f(0) =f(2)=0 f'(x)&gt;0 on(- infinty,1) f'(1)=0 f'(x)&lt;0 on (1 , infinty) f"(x)&lt;0 on(-infinty…

Q: Find the volume of the solid bounded by the paraboloids z = −7 + x² + y² and z = 4 − 2x² – 2y² 1300

A: The given paraboloids are: z=-7+x2+y2     and    z=4-2x2-2y2

Q: 1. Determine the area bound by the following functions and double- check your answer.. y = 4x² + 1,…

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Q: If f(x) and g(x) are continuous functions and use the table below to evaluate c'(-1). x -2 -1 f(x)…

A: Consider the table