Find the vertex of the pairabola F(x)=x²+3x+1₂

Q: find the domain of the vector function r(t)=⟨√(t^2-1,log⁡〖(t^2-3t+2),1/√(-t)〗 )⟩

A: The solution is shown in step-2

Q: b. √3/2 dr ܐ1 || arcsin ܗܘܐ 6 2 ܀

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Q: Find the area of the region bounded by the graphs of y = 1 + 3x, y = 8, x = 2 and x 3.

A: To find the area of the region bounded by the graphs of  and Note: Since the student has posted…

Q: For a given commodity and pure competition, the number of units produced and the price per unit are…

A: Using integration, we can find the consumer surplus and producer surplus.

Q: Find r(t) if r' (t) = ti+etj+tet kand r(0) = i +j+k

A: To find:r(t)

Q: Determine whether the sequence defined by an = 5+2(-1)" converges or diverges. If it converges, find…

A: The given sequence is .We have to determine whether the sequence converges or diverges.

Q: Find the radius of convergence, R, of the series. R = 4 n = 1 747 Find the interval, I, of…

A: The series is

Q: Complete the table by computing f(x) at the given values of x. (Round your answers to three decimal…

A: The limit of a function at a given point is the value of the function as the input approaches the…

Q: Find the trigonometric integral. (Use C for the constant of integration.) /t tan(0) sec5 (9) de

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Q: Consider the function f(x) = 2x³ – 15x² + 36x +1 over the interval [1,4]. Which statement in below…

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Q: Evaluate cos 4θ in terms of the power of cos θ only. In doing so, follow the steps below and…

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Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: A manufacturer of handcrafted wine racks has determined that the cost to produce  units per month is…

Q: Calculate all four second-order partial derivatives of f(x, y) = sin(x² + y2) and check that…

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Q: Find the area of the surface. the helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v)i…

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Q: Evaluate the surface integral. [[ye y dS, S is the helicoid with vector equation r(u, v) = (u…

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Q: Find the arclength of a = 3y/2 on 3 ≤ y ≤7, to three decimal places.

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Q: Two spacecraft are following paths in space given by r₁ = (sin(t), t, 1²) and r2 = (cos(t), 1-t,…

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Q: Express the limit lim n→∞ n Σ(4(a)² - 2 (2:)) Aa over [-1, 1] as an integral. 0 i=1 Select the…

A: The definition of a definite integral in terms of sum and limits is given by:…

Q: use Implicit Differentiation to find at the given point on the curve. √√x+√√y=3 at the point (1, 4).

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Q: Find the area of the surface obtained by rotating the curve y = from x 0 to 2 about the x-axis. = =…

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Q: tan X -dx 2 x² +1

A: Given Integral As we know that

Q: Use the theorem given below to find the curvature of r(t) = √6t² i + 2tj + 2t³ k. Theorem: The…

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Q: Find a formula for y' and determine the slope y'Ix-3 for the following function. -8ex -7ex +4 y =

A: To find a formula for and to determine the slope  for the following function.

Q: A ball is kicked into the air so that the path of its flight can be modelled by the function, where…

A: x(t) = -4.9t² + 9.8t + 5

Q: 1) Find the derivatives d (a) dt ( Co d (b) dr cos(2³) dz + 35t arctan(t) dt

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Q: lim x → 1- INT(x + 4) =

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Q: Find y=x-3 dx dx 11 ㅁ

A: we given function

Q: Find the exact values of the six trigonometric functions at the angle a = -120°. If any are…

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Q: Evaluate f(x + y)ds where C is the straight-line segment x =t, y = (3-t), z = 0 from (0,3,0) to…

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Q: Let f be defined as follows. y = f(x) = x² - 9x (a) Find the average rate of change of y with…

A: Given that      y = f(x) = x2 - 9x

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Consider the following demand function: p = D(x) Step 1 of 2: Find the elasticity function. =…

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Q: * Incorrect. The figure below shows contours of g (x, y) on the region R, with 5 ≤ x ≤ 11 and 4 ≤ y…

A: The solution is shown in step-2

Q: Find all solutions to the equation e²x = 4 - ²x I

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Q: Find an equation of the plane that passes through the points (2, 4, 1), (2,2,-4), and (−3, 5, 3).

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Q: 23, Find an equation of the tangent line to the graph of the function at the indicated point (², 1)…

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Q: Consider the following function and closed interval f(x) = √6-x, [-19, 6] 10 617

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Q: Suppose y = sinh-1x. Then 1 sinh X - sinh(y) O arcsinh(g) Oy= x= = sech(y) 1 X Using implicit…

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Q: Problem 2.. Find an equation of the plane that passes through the point (1, 0, -3) and contains the…

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Q: A manufacturer of handcrafted wine racks has determined that the cost produce x units per month is…

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Q: The rabbit population at the city park increases by 17% per year. If there are intially 196 rabbits…

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Q: The total U.S. personal income I (in billions of dollars) from 1960 and projected to 2024 can be…

A: Given:We are required to find:

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 4n²+3…

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Q: An arrow is shot into the air so that its horizontal velocity is 37.0 ft/sec and it vertical…

A: Given Horizontal Velocity component = 37 ft/secVertical Velocity component = 11 ft/sec

Q: For the following vector, v, find ||ull, the unit vector with the same direction angle as v. --- O…

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Q: Compute the given integral. 9x - 4 9x² - 8x - 1 S dx +C

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Q: et f(r) be the function 107² +9r+ 5. low the steps below to use the formal definition of the…

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Q: What is the purchase price of a 50-day T-bill with a maturity value of $2,040 that earns an annual…

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Q: Evaluate the following limit (if it exists): √√x-x² 1-√√x lim- x-|

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Q: Find the nth derivative of the function: y = xe*. n+1 b) x²+¹ ex c) (x+n) e* a) x*e* d) x¹ ex

A: Given the function is .