5. Consider the region R bounded by y=1-x² x = 0 and y = 0 [This region is used to answer questions a - e] Draw a graph of the region a. b. Find the area of the region. Exact value solutions only.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

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Q: Find lim 1 2x217 a. x→ 0* 5 (x-6)2/7 b. x→ 0 as C. X→ 6* d. x→ 6

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Q: 1 When is the velocity of the particle positive? When is it negative? When is the particle speeding…

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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: For the following telescoping series, find a formula for the nth term of the sequence of partial…

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Q: (2). z=x² + y,k=-4,-1,0,1,4.

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Q: Given Cost and Revenue functions C(q)=q3−11q2+55q+5000 and R(q)=−3q2+2400q​, what is the marginal…

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Q: Calculate the iterated integral. 1 6 L' [lx-ethox (x + e-x) dx dy + 10

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Q: Consider the following power series. Let a = lim LIM R 11 (-1)*(x-8)* ku 11k (-1)* 11k (x-8)*. Find…

A: Solution will be given below

Q: Find the equation of the line tangent to the graph of f(x) = (In x)5 at x = 5.

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Q: x(t) = Find a plane containing the point (4,7,-4) and the line y(t) z(t) = = −4+t 2- 7t - 38t

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Q: The total cost of producing x laser pointers is C(x)=10+√(3x+24) Find the marginal cost at each…

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Q: Find the parabola of the form y = ax² + b which best fits the points (-1,0), (2, 2), (4,4) by…

A: Given sum is S=(a+b)2+(4a+b-2)2+(16a+b-4)2

Q: Given that the acceleration vector is a(t) = (−1 cos (−1t))î + (−1 sin (−1t))ĵ + (−5t)k, the initial…

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

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Q: Justify parts a-d with a 2) Given: f(x)=x+3 a) Find all intervals of increase and decrease. b) Find…

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Q: An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will minimize…

A: Let the base height and length be x and the height be y.Given: the volume is 4 cubic feet.

Q: The price, in dollars per units, that consumers are willing to pay for a popular high-end digital…

A: Algebra

Q: Find the point on the line 3x + 6y +2=0 which is closest to the point (2,-2). Answer is

A: Foot of perpendicular

Q: Please help (41-45)

A: Here we have to find the derivative.

Q: You invest ​$1500. If the account grows by 5.7​% per​ year, how quickly will the account be growing​…

A: Please see the below picture for detailed solution.

Q: Find all critical points of the following functions. a. f(x) = -r² + 10x + 43 b. g(x) = ¹/3 c. h(r)…

A: To find the critical points for given function

Q: 2. a. Write a degree 3 polynomial in factored form with integer coefficients with zeros 6/and. b.…

A: Given :- Zeros of degree 3 polynomial are 6i and 45

Q: The diagram above shows the graphs of y = e-* (red) and y = x (blue). (a) State the equation in x…

A: Point of intersection refers to the point where the graphs intersect. Graph is a diagrammatic…

Q: Find the volume of the solid generated by revolving the region bounded y = sin x, y = 1 on the line…

A: To find the volume of the solid generated by revolving the region  bounded by y=sin x, y=1 on -3π2,…

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

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Q: Complete the following stepts in order to find a vector-valued function r(t) that satisfies the…

A: Given r''( t ) = -32j r'( 0 ) = 2003i + 200j r( 0 ) = 0

Q: Compute the product. This exercise should be done using technology. (If an answer is undefined,…

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Q: Consider the vector field F and the curve C below. F(x, y) = (2+ 8xy²)i + 8x²yj, C is the arc of the…

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Q: Which of the following numbers is imaginary? A 3+(-√18) B √(-3)(-4) C -√2+√√-4+7 D 5-√6-8

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Q: find the volume of the solid revolution generated by revolving the region bounded by y=e^(3x) y=3…

A: Given curves equations:- y=e3x,y=3,x=0

Q: As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a…

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Q: Express these decimals in short form using the bar to designate the repeating part. Find the…

A: We can solve this as follows:

Q: Write the equation of the line in the point-slope form that passes through the points (0,8) and…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the equation of the curve for the given slope and point through which it passes. Use a graphing…

A: equation

Q: Mr. Brust is running down his street. His position is given by the function p(t), where t is…

A: Mr. Brust is running down his street. His position is given by the function pt,  where t is measured…

Q: Average Life Span One reason for the increase in human life span over the years has been the…

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Q: Evaluate the following limit. lim 1+ X→∞ lim X→∞0 1 2 3 X 2 3 X In x Inx = (Type an exact answer.)

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Q: 1. Given that y² = 48sin 0 and dy/dt = -5, find de/dt when 0 = TT/6

A: Given y2 = 48sin(thita) dy/dt = -5 thita = pi/6

Q: A certain magical substance that is used to make solid magical spheres costs $600 per cubic foot.…

A: As we know that Area of sphere( A ) = 4πr2Volume of sphere( V ) = 43πr3

Q: PLS do fast within 5 minutes and i will give like for sure Solution must be in typed form The…

A: How can both x-intercept s be determined if the equation y=-(x+6)(x-3) is given?

Q: A roadside wall has a zigzag pattern on it as shown. The two longest lines are each 2 m long, then…

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Q: This function: 24 4 -4 -2 0 -2 -4 has a jump disco has an infinite di

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Q: A projectile is launched straight up in the air. Its height​ (in feet) t seconds after launch is…

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Q: Use l'Hôpital's Rule to evaluate lim t→0 lim t-0 5 sin (416) - 4t = 5 sin (416) - 4t (Type an exact…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: By using implicit differentiation to find an equation of the tangent line  to the curve at the given…

Q: Find the distance from the point (-4,-6,4) to the line a(t) = ( – 5, 1, − 3)t + (− 7, — 4, 7) FORCYY

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Q: Determine the amplitude and period of the function s(t) = 0.4cos(t + pi ) + 9 without graphing the…

A: Determine the amplitude and period of the function s(t) = 0.4cos(t + pi ) + 9 without graphing the…