Consider the region bounded by the parabolas: y : x² + 4x + 3 and y = x² + 2x + 3. the volume of the solid region is revolved about Calculate when the the x-axis.

Q: 1. The graph of f(x) is shown to the right. On the same grid, draw a sketch of f'(x).

A: Since you posted multiple questions, I need to solve only first question.

Q: The equation of the line that goes through (3, 2) and (-7, 10) can be written in the form y = mx +…

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Q: 8) A region is bounded in the second quadrant by the curve y = In(1-x), the line y = 3, and the…

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Q: consider the region bounded by the parabolas: y=x² + 4x + 3 and Find y = - x² + 2x + 3 the area of…

A: The region bounded by the parabolasy=x2+4x+3 and y=-x2+2x+3

Q: Compute 1. x²ex³dx.

A: ∫-∞0x2ex3dx

Q: (b) Find the co-ordinates of the turning points of the following function: y = 3x4 - 16x³ + 24x² -…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = [x(t) 3t² ly(t) = 10 + 1t =…

A: x(t)=3t2.......(i) y(t)=-10+t......(ii)

Q: Consider the series Answer: L = n=1 5" (n+1)4²n+1* Evaluate the the following limit. If it is…

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Q: Given the set of parametric equations of a curve C defined by [0,5). x = ln(cost), y = sint, te 1.…

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Q: In this problem, x = C₁ cos t + c₂ sint is a two-parameter family of solutions of the second-order…

A: We will find the general solution .

Q: Find all values of m so that the function y = emx is a solution of the given differential equation.…

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Q: 3π Plot the point whose polar coordinates are 2, 2 -5 -4 -3 -2 -1 5 4 3 2 1 -1 -2 -3 -4 V 1 2 3 5

A: The given polar coordinate point2, 3π2. We have to plot the point in the rectangular coordinate…

Q: Find the first partial derivatives of the function. f(x, y) = x³ + 6xy7 fx(x, y) fy(x, y) 11

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Q: Use integration by parts to find the integral. (Use C for the constant of integration.) [x² In(ax)…

A: We have, ∫ xnlnax , where a ≠0 , n≠-1

Q: Use the half-angle formulas to find the exact value of the trigonometric function. Simplify your…

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Q: 2) Suppose the vertical position of an object is y(t) = 32t - 8t², where y(t) is measured in…

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Q: Construct a limit evaluation problem with an answer of 1.

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Q: 8 2k Σ k=1 k!

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Q: 1. 2. Find f'(x) and f"(x). Determine the following Domain a. b. x and y intercepts t. The critical…

A: derivative calculated by differentiation with respect to x

Q: Biologists have noticed that the chirping of crickets of a certain species is related to…

A: T=Temperature in degree FahrenheitN=Number of chirps per minute

Q: Given the function f(x) = 18x + 3, determine the intervals where increasing and decreasing, and the…

A: The function  fx=-2x3-12x2-18x+3⇒f'x=-6x2-24x-18=-6x2+4x+3=-6x+3x+1⇒f''x=-12x-24=-12x+2

Q: Solve the differential equation (D²-1)y=(e²=+1)

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Q: fa 2D Free-body diagram has four unknown support reactions, the problem is: Statically Determinate O…

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Q: 1. From a piece of cardboard that is 24 cm by 48 cm, cut equal squares out of the comers. Foldup the…

A: Let side length x squares cut from each corner of cardboard Objective:-To find the maximum volume…

Q: Find the unit vector ey, where v = = (4,0,7). (Give your answer using component form. Express…

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Q: 4) Suppose the velocity of an object is v(t) = 9t-t³, where v(t) is measured in feet per minute.…

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Q: A manufacturer has been selling 1150 television sets a week at $420 each. A market survey indicates…

A: Given :- At $420, A manufacturer sold number of televisions are 1150. And at $21 rebate offered to a…

Q: olve question 2 please. Explain in an easy to understand way

A: Graph of f(x) is given . We have to find why the derivative of a sinusoidal function is also going…

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: r=135 in h=168 in Rate of increase of radius=1.2 in/sec Rate of decrease of height=-2.8 in/sec

Q: Find all the second partial derivatives. f(x, y) = xy - 4x5y² fxx(x, y) = fxy(x, y) fyx(x, y) = =…

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Q: ) Based on your experience in parts (a) and (b), conjecture an antiderivative for each of the…

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Q: Find the area of the Polar Region located in the interior of the graph of r = 8 - sint A = 2√²/²2…

A: The polar equation r=8-sint Graph

Q: Suppose you deposit $10,000 into a savings account that earns 3.5% interest compounded quarterly.…

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Q: Consider the series Find S4 and S4= S8 = S8 n=1 3 n+7 43 Let Sn be the n-th partial sum; that is, Sn…

A: Given:  We have  Sn = 3/n+ 7  , limit series n =1 to infinity

Q: Let r₁(t) = (-7, -6, -3) + t(0, 2, -3) and r₂(s) = (5, -10,-5) + s(3, 0, -2). Find the point of…

A: We want to find the point of intersection of the given two lines.

Q: Sketch the graph of the following parametric equations. a. x = 4, y = sint b. x = e^t, y = e^2t, t ∈…

A: a) x=4 ,y=sint b) x=et,y=e2t ,t∈[0,∞) c)x=3sint,y=4cost ,t∈0,pi

Q: Evaluate. Use reduced fractions instead of decimals in your answer. 7 sec 6x dx = ² S + C

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Q: Second derivative of f(x) =2^x/x

A: To find the second derivative of the following function. fx=2xx

Q: Using the definition of the derivat to find the derivative of the following function. f(x) = x² ;…

A: a) f(x)=x2 b) f(x)=1/2 c) f(x)=sqrt(x) Find the derivative by definition.  According to bartleby…

Q: Suppose that the marginal revenue for firefighting protective clothes is MR = 258 - cost is MC =…

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Q: lim Δx→0 3 1 x + Δx Δε 1 της X

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Q: Construct a related rates problem where the answer to said problem is 1.5 Please make the problem…

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

Q: Find all values of m so that the function y = emx is a solution of the given differential equation.…

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Q: Find the area of the parallelogram whose vertices are given below A(-1,4) B(4,0) C(9,3) D(4,7) The…

A: We have, A(-1,4) , B(4, 0) , C(9,3) , D(4, 7)

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A: The curve of intersection of the parabolic cylinders x = y2 and z = x2 at the point (1, 1, 1). Find…

Q: graph to the left (in black) gives f(x), while the graph to the right gives g(x) (which is constant…

A: ddxfgxx=30

Q: (a) The series For the following answer blanks, decide whether the given sequence or series is…

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Q: The following graph of the function f satisfies lim value of 8 >0 such that the precise definition…

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Q: Use the chain rule to find dw dt dw dt W = In (√x² + y² + z²), x = 9 sin(t), y = 8 cos(t), z = 5…

A: W=lnx2+y2+z2 x=9 sin(t) y=8 cos(t) z=5 tan(t)

Q: Determine whether the three points P = (-5, -4,-3), Q = (-8,-10, -12), R = (-11, -15, -21) are…

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