Find a set of parametric equations for the curve of intersection of the paraboloid z² +4y² -z = 0 and the plane 2r -z = 0.

Q: 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. HI-4 (a) lim f(x)g(x) #114 (b) lim…

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Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

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Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Find the area bounded by the curves y = x(x − 1)², y — axis, and the line y = 12.

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Q: 6. f(In x)² dx

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁749 dx…

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Q: y = (x² + x + 1)²

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Q: 10. Given the graph below, what is the value of x of the function H(x) is discontinuous? h(x)== A. 0…

A: Since you have asked multiple questions,  we will solve the first question for you. If you want any…

Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

Q: Find the Area of the Surface obtained by rotating the curve about the y y = √√x, 1 ≤ y ≤2

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Q: A certain family in Sitio Calculus opened a t-shirt business last year. The family started with 50…

A: Given: fx=x2-2x+3 Since, the marginal cost function is the derivative of the total cost function,…

Q: Let L(y)=(x-1)y" - xy + y a) with the observation that y, zx is a solution of L(4)=0 on (1,00), by…

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Q: Let The coefficient of x³ in the Maclaurin series for f(z) is: Answer: . You may explain your answer…

A: The given function is f(x)=9e2x-x A Maclaurin series is given by:-

Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all f'(c)…

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: Given Cost and Revenue functions C(q) =q³-9q² +57q+5000 and R(q) = -3q² +2600q, what cost is…

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Q: Let P be the point with Cartesian coordinates (6, 9), and C be the plane curve with parametric…

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Q: Solve f(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: Solved below.

Q: Suppose that f(x) = x² − 3x + 2. Then there is no critical number to determine concavity. Select…

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Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t == . — = dt

A: Given:ds/dt=10csc^2(2t) To find: solution at s=2 and t=π/4

Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

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Q: Find the distance from the point P(1, 2, −1) to the line passing through the points A(−2, −3, −5)…

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Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: Let (t) = 5 cos(t) and y(t) = 3 sin(t) All answers should be decimals rounded to 2 decimal places.…

A: Applications of differentiation

Q: Find f. f(t) = f"(t) = 5et + 6 sin t, f(0) = 0, f(T) = 0

A: On solving this we will get

Q: dx x√x-1 dx √8+6x-9x² 3. S 4. S

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Q: _ ²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8 Given x =

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Q: THE AREA BOUNDED BY THE PARABOLA y² + x - 2y = 1, THE X-AXIS, AND THE REVOLVES ABOUT THE LINE LINE…

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

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Q: T. (3x² - 4x¹ + 2)dx -1 -3

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Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 Cos 0 Er = g(0) = 12/250c4 D:r=3 (1.) Show…

A: Let's solve part 3 and 4.

Q: P N

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Q: 4. Verify the final value theorem for the function 3t²e-4t and determine its steady state value.

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Q: Find the area bounded by the parabolas (x-2)²-9py = 0 and y² = 9p(x-2).

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Q: 1) Find |R'(t)|, Make sure to simplify your answer 2) Find the distance traveled by a particle…

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Q: y Let line l: x == and point P(1,0,1). 2 3 ● Find the parametric equations of the line parallel to…

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Q: Compute 4 sin(TTX) d dx A. 4 sin(TTX) B. 4sin(TTX) In4 C. 4sin(x) (πIn4).cos(TTX) D. 4 sin(TTX)…

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Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with…

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Q: 7. Use Disk Method to find the volume of the solid generated by revolving the R bounded by y =√x =…

A: Given that Region bounded by y=1x+1,x=0,y=4Revolving about x axisUsing washer/disk mathod…

Q: closed box with a square base is to contain 252 cubic feet. The bottom costs $5 per square ot, the…

A: Please refer to the image below

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: This question can be solved using the concepts of application of derivatives.

Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: Starts the domain, vertical asymptote, and end behavior of the function.  g(x) = ln(3x +21) + 1.5…

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Q: 1. The derivative of a constant is equal to A. -1 C. 1 B. 0 D. 2 2. If ƒ(x) = −5π, then ƒ'(x) is…

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Q: Find the transition points. y = 5x³ + 120x² (Use symbolic notation and fractions where needed. Give…

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Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy