Given the quadratic expression p(q) = 2 − r² + 4q −4 − 7q+8q² - 10r, identify and state the values for a, b and c.

Q: - Find the area of a triangle PQR, where P = (1, - 2, 3), Q = (1, — 4, 1), an R = (1, 6, 0)

A: we need to find out the area of the triangle whose vertices are given.

Q: nd the area of the region enclosed by the curve y = x² +2, the x-axis and the lines x = 0 dx=1.…

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Q: 5. Let f(x) = 3x³ + 2x + x+ 1 x²+x-2 . What types of asymptotes does f(x) have? horizontal and…

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Q: Compute the length of the curve r(t) = (-8t, 3t — 8, —8t + 7) over the interval 0≤t≤8 L =

A: To compute the length of the curve  overthe interval .

Q: Use the definition to find the Taylor series (centered at c) for the function. f(x) = ex c = 0

A: The given function isThe centered value is

Q: Given a constant, the matrix A [3] column vector cos sin 0 on the left, like this sin 0 is a…

A: The objective of this question is to prove Green's theorem for various cases and to verify the…

Q: Evaluate the improper integral and state whether it converges or diverges. Show limit notation and…

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Q: Calculate ff f(x, y, z) dS For Part of the surface x = 2³, where 0 ≤ a, y ≤ 13-1; f(x, y, z) = I s…

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Q: Find the absolute extrema of the function (if any exists) f(x)=x^3ー21 (0,2)

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Q: -example 2- Prove the limit using the epsilon-delta definition of limit. lim(2x+3)= 13 x-5

A: The limit of f(x) at x=c equals L if, for any ε>0, there's a δ>0 ensuring that when the…

Q: Solve cos(8) decimal places. 0 0.2 for solutions on the interval 0 ≤ 0 < 2. Write your answer(s) in…

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Q: Find the exact area of the region bounded by the given curves. Show a detailed sketch with the…

A: To find the exact are of the region bounded by the given curves.

Q: At YasterMart, people are willing to buy a pounds of chocolate candy per day at $p dollars b per…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Find the equation of the tangent line to the curve y = The equation of this tangent line can be…

A: The objective of this question is to find the equation of the tangent line to the curve y = 4 sin x…

Q: Let h(x) =tan(3x + 5). Then h' (4) is 3 sec² (17) 2 and h''(4) is

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Q: (a) The graph in the figure given below is made of line segments joined end to end. At which points…

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Q: Find the derivative of the function by the limit process. Find an equation of the tangent line to…

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Q: Let C be the curve y = 7- 6 5 4 3 2 1 @ B +e 3 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Find the surface area…

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Q: Use the definition to find the Taylor series centered at c=0 for the function f(x) = sin(3x) Select…

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Q: Consider the plane with equation x + 2y + 2z - 6 = 0. Determine the point on the plane that is…

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Q: 1. The acceleration due to gravity, g, varies with height above the surface of the earth in a…

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Q: Match the vector coordinates to each Cartesian vector. y M D B -4-20 с U G X -4 W 14. CD 15. JK 16.…

A: We need to find the coordinates and magnitude of the vector.

Q: A circular swimming pool has a diameter of 16 m, the sides are 4 m high, and the depth of the water…

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Q: Find the length of the curve correct to four decimal places. (Use a calculator or computer to…

A: The given curve equation The length of the curve for  is

Q: 4. (20%) Derive the quotient rule du dv V -U dx dx V² dy dx = (la) if y = 40 (1b)

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Q: Find the limit, if it exists, or type N if it does not exist. (x + 25y)² x² +25²y² lim (x,y) →(0,0)

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Q: If 3y² + x² = −3 − 3x then find dy in terms of x and y. modta If 4x² + 2 = 3y - 5y² then find in…

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Q: Solve the profit maximization problem of a competitive firm max II(q) = pq-C(q) 9 subject to q≥0…

A: The objective of the question is to find the quantity (q) that maximizes the profit function II(q) =…

Q: The point (-13,-12) is on the graph of y= f(x). a) A point on the graph of y = g(2), where g(x) = —…

A: Given: The point  is on the graph of .To Find: (a) To find the point on the graph of , where .(b) To…

Q: integral test ∞ (α) Στ n n=1 8 b) 6) Σ n=1 -|~1/2 η2

A: To determine whether it is Convergent or Divergent using the integral test.

Q: d. Ek-2h(k) e.Ek=19(k)h(k)

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Q: 2) Calculate the following: 1 0 0 Xp 6:90- 0 1 0 Ур 001 Zp/ =?

A: ⎝⎛​xp​yp​zp​​⎠⎞​Explanation:     ⎝⎛​100​010​001​⎠⎞​⎝⎛​xp​yp​zp​​⎠⎞​…

Q: Solve the given differential equation by variation of parameters. x²y" - xy' + y = 8x y(x) = ,X>0

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Q: 2. Consider the function: (a) Calculate Vf at the point (0,2). Vf(0, 2) = f(x, y) = y² sin(3x) + 5y…

A: The objective of the question is to calculate the value of the function Vf at the point (0,2) and to…

Q: The probability of precipitation in a California city varies from a peak of 0.38 (38%) in January to…

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Q: 22. Determine the area of AABC with vertices A(3,-2,4), B(1, 3, 2), and C(-1,2,4).

A: we are given three vertices of a triangle and we need to find its area.

Q: apply either the Alternating Series or Ratio Test To solve for these series

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Q: (a) √ √²(1 + √I) dx (c) 2²√2²-25 dz dx (d) / cos²x dz dx

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Q: Find any points of inflection and discuss the concavity of the graph of the function.

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Q: 28 :) P = = 5² Squared directly with Z=2 and inversely J 2=4 IP P = 2² when 28 5 P when == 2 and r =…

A: p varies directly as the square of z and inversely as r. p = k .............(1)Where k is constant…

Q: Find a parameterization for the curve y = 6 + 2x¹ that passes through the point (0, 6, -5) when t =…

A: To find the parameterization of the curve

Q: Approximate cos COS a = h = 12 by using a linear approximation with f(x) = cos x. ≈ f(a) + f'(a).h =…

A: The given function is .

Q: For the following series, apply either the Geometric or p-Series Tests, where appropriate. 15 (2) Σ…

A: The given series,(a) (b) (c) (d) The objective is to check the convergence of the series by using…

Q: (a) x6 (b) x² - 4 + 4x² + 16 + Ax + A x - 2 te (x² − x + 1)(x² + 9)² B -x+ + + B x + 2 Cx + D 2 '+9…

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Q: find the function interpretation of the series Σn_1 n x³n

A: To find the function interpretation of the following series.

Q: Find the linearization L (x, y) of the function f (x, y): = L (x, y) = 68 - 1x² - 4y² at (4, -3).…

A: The linearization of f(x,y) at (a,b) is given byL(x,y) =f(a,b) +fx(a,b)(y-b)

Q: Peter wishes to create a retirement fund from which he can draw $40,000 when he retires and the same…

A: The objective of this question is to calculate the present value of an annuity due, which is a…

Q: To find the arclength of y = 2x²-1 from x = 0 to x = 4, which is the correct integral? 4 = Sº OL=…

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Q: 2 X 2 X 0+ - 4 +4 dx =

A: C+C

Q: 20. Given a = [3, -5,1], b = [-2,4,-1] and 2 = [7,3, -2], find a) b.č b) axč c) , the angle between…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub parts…