2. a) Evaluate the integral. sin(3nt)dt b) 2x³ +3x6 dx

Q: [ f(x) dx 3 Given that 1 ≤ f(x) ≤ 4 for 3 ≤ x ≤ 7, estimate the value of ] ≤ [ f(x)da <

A: Estimated value formula m(b-a)&lt;=int_a^b f(x) dx&lt;= M(b-a)

Q: an n In n en (domain n ≥ 1)

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Q: Use the formula T = T(t) = [r'(t) = r²(e)] - '"(t) x Ir'(t) x r"(t)|2 T(0) = r(t) = 7t, to find the…

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Q: J 3x ex dx

A: The given integral, ∫3xexdx. We have to solve this integral.

Q: In a particular city, taxicabs charge passengers $2.20 for entering a cab and then $0.50 for each…

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Q: Suppose the demand function for a product is given by the function: D(q) = -0.02q+98 Find the…

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Q: which value (s) {5,7,9,11,13}make the inequailty w-4<8 true?

A: The inequality is given and we need to solve it.

Q: 2. Locate all local extrema and saddle point(s) of f(x, y) = xe cosy for (x, y) = (-T, T) x (-π, π).

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Q: A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off…

A: dθdt=0.1 rad/min In ∆ABC…

Q: 1. Verify that y = e²x — e-* −1 is a solution for y" - y' -2y = 2

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Q: What is 7.8% of 220

A: X % of Y = Y × x100

Q: Given the function f(x) = -2x³ +96x + 1, determine the intervals where the function is increasing…

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Q: egral, if it converges. If it diverges, F

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Q: If a company has total costs C(x) = 40,000+ 15x + 0.2x2 and total revenues given by R(x) = 595x…

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Q: 4. Determine the 75th derivative of each of the following functions. f(x) = 3 cos 2x b)

A: given function is f(x)=3cos(2x) we know d dx(cos(ax))=-asin(ax)  and d dx(sin(ax))=acos(ax)

Q: The growth of a colony of bacteria can be described by exponential growth. If the colony initially…

A: Pt=P0ert⇒P0=initial population⇒r=Growth rate⇒Pt=Population at time t⇒t=time in hours

Q: 1. Consider the following vectors a= [1, 3, 2] & b = [-2, 2, 1] a. Draw each vector on a grid b.…

A: a→=1,3,2 ,b→=-2,2,1

Q: 4. Graph f(x)=-2log, (x-5)+3 Show your work.Write Domain and range.

A: According to  question,given function,fx= -2 log3x-5+3

Q: Find the critical numbers and any local maximum and minimum points for the function Find exact…

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Q: y = 1/(x² + c) is a one-parameter family of solutions of the first-order DE y' + 2xy² = 0. Find a…

A: y=1x2+c is a one parameter family solution of differential equation:  y'+2xy2=0.Initial condition…

Q: the two-dimensional object. An oversized hockey puc = g _52+6. 495 2

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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 following definite integrals: x² 1+r (1) L'a (3) ₁ (x³ arccos x + xe do Jdx (4) (2) # √ ²…

A: Note :  Since you have posted a question with multiple subparts, we will provide the solution only…

Q: Find the present value of a continuous income stream F(t) = 20 + 8t, where t is in years and F is in…

A: To find the present value of a continuous income stream Ft=20+8t, where  t is in years and F is in…

Q: Suppose that R is the finite region bounded by y = x, y=x+2, x=0, and x = 4. Find the exact value of…

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Q: 5. The golf ball manufacturer, Pro-T, has developed a profit model that depends on the number x of…

A: To find : maximum profit and values of x and y to maximize it.

Q: Compute the dot product. (Use symbolic notation and fractions where needed.) ( ²1₁ 212 ) · ( 5₁ -1)…

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Q: f(x, y) = e cos(ly). Find and classify all critical points of the function. If there are more blanks…

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Q: Let h = f o g where ƒ : R² → R and g : R² → R² is defined by g(x, y) = (–3x²y, y − 2x). Find the…

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Q: given fal = √√x-5 and 9(x) = x² + 4x + 2 Find Fog and g of

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Q: 2. Determine the cartesian equation for a line that passes through the point (4,-3) and is…

A: The line passes through the point 4,-3 and is perpendicular to the line r→=2,-3+t5,-7 Therefore, the…

Q: 1/3 The integral fo²³ 3-√2-9x1² dx is to be evaluated 0 directly and using series approximation. 1)…

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Q: Which of the following are separable differential equations? A. y = 2x - 3y +1 B.(4)=x+y □ C. 2xydx…

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Q: Evaluate the double integral cos √√x² + y²dA, where D is the disc with center the origin 。 and…

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Q: If land that can be farmed L is eroding continuously at a rate of 4.5% per year because of changing…

A: “Since you have asked multiple questions (a and b are not related to each other), we will solve the…

Q: 6. Write out the series and find the sum: Σ= 2(k − 1)(2k – 1)

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Q: Find all the first and second order partial derivatives of f(x, y) = 6 sin(2x + y) — 2 cos(x − y).…

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Q: Quadratic equations are not nol in the form f(x) = ax²+bx+c to find (h, k). Begin by completing the…

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Q: A plant with a mass of 10 kg is suspended from a ceiling by two lengths of rope that makes angles…

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Q: Find the value of k such that the limit exists x² kx + 4 lim x-1 - x - 1 The k value is The limit is…

A: We have  function (x2-kx+4)/(x-1) We have to find value of k for limit existence when x tends to 1…

Q: If you want to earn 7% annual simple interest on an investment, how much should you pay for à note…

A: A = P (1 + rt) Where  A -  Accumulated amount              P -  Principal amount              r -…

Q: 3. Determine the absolute extreme values for the function Y=3sinx + 4cosx on the interval [0,27]

A: y = 3sin x + 4cos x ,on the interval [0, 2pi]

Q: Determine a definite integral that represents the area of the region enclosed by one petal of r = 4…

A: We have,      r = 4 sin (3θ)       a = 0

Q: Find the point at which the line meets the plane. x= −3+6t₂ y = −4+5t, z= −3+4t, x+y+z= -25 The…

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Q: An espresso stand finds that its weekly profit is a function of the price, , it charges per cup. If…

A: An expresso stand finds that its weekly profit is a function of the price, x,…

Q: 1a Differentiate the following functions with respect to t and simplify your answer as far as…

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Q: Find a Cartesian equation relating and y corresponding to the parametric equations Write your answer…

A: x=3sin6t ,y=6cos6t

Q: If z = (x + y)e³ and î = u² + v² and y = u² — v²,

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Q: D is the region enclosed by the parabolas = 2 -2 2 = y² - 1 and 2 = x = y² + 1.

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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