9. Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is dx 100 5000 (₁ (calculators/week). dt (Notice that production approaches 5000 per week as time goes on, but the initial production is lower because of the workers' unfamiliarity with the new techniques.) Find the number of calculators produced from the beginning of the third week to the end of the fourth week. - (t+10)²

Q: 4. Consider the plane : x + 3y - 2z = 6 and the line with parametric equations l: x=4-3t, y=2+t, z =…

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Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

A: Given: y=x2+5 Graph of the functions given are

Q: Enter a whole or decimal number, or DNE for does not exist or undefined. |0x| lim (5+10=¹). [ - -0+z

A: Topic = Limits

Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

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Q: 2- Compute 1+i 2-51

A: Given that,      1+i2-5i

Q: 23. Test the series below for convergence using the Ratio Test. Σ n2²n 8n-1 n=1 The limit of the…

A: Here we have, ∑n=1∞n22n8n-1

Q: Suppose g(z) zn 2nn n=1 Σ Solve for the value of the integral 1 2-₁ / e²g² (2) dz 2πi |2|=1 using…

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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: i can't understand your solution

A: We have to explain the solution.

Q: Find the equations of tangent and normal lines of the curves at given points: y²-3xy - x = 0 at(2,8)

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Q: cos 3x cos 4x dx

A: ∫cos3xcos4xdx here we use formula  2cosxcosy = cos(x+y) +cos(x-y) here x = 4x      y = 3x

Q: P N

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Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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Q: Give the general form of the equation of the plane that is perpendicular to the plane x+2y = z + 5…

A: equation of line

Q: y = (1+x)² 2 x² 2

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Q: Given: parametric curve H defined by r(t) = tan-¹t and y(t) = eªt, where t = R (a) Find the slope of…

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Q: A homework problem asks for a sketch of the graph of the inverse of f(x) = x + cos x. Frank, after…

A: Given ,  A homework problem asks for a sketch of the graph of the inverse of f (x) = x + cos x…

Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

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Q: Given x = y³+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 B

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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: Determine the value of x when the slope is its maximum for the function f(x)=2cos(3x)

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Q: If z is a function of x and y implicitly defined by əz əz find and əx ду at (x, y, z) = (0, 2, -1).…

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Q: 156. Find the area of the region D, bounded by y = √4x², x= √3, which is the region x=2, and y = 0.

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Q: 2. Verify using the principle of Superposition that y₁ = ²* and y₂ = e* are solutions of y" - 7y'…

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Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

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Q: √√f(x) x→ 3.h(x) 20. What is the value of lim A. C. - 12/2 6 B. -1 D. 21/2 5 I N|2 13 -?

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Q: Determine the center-radius Form of the equation of the sphere whose diameter has endpoints at (2,…

A: The first question has been solved as per the request of the student.     The center radius form of…

Q: 1- Find the inverse of 2=2-51.

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Q: & 38. Evaluate: √x dx A. x4/3 + C 3 4 C. ³x5/3+C B. x³/4 + C D.x3/5 + C 39. Evaluate: fx(4x - 3)dx…

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Q: Find a particular solution of =(x−1)² if y=-21 when x=-3. dx

A: dydx  = ( x - 1 )2   , y = -21, x = -3 we have to find particular solution of it

Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

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Q: 43. Evaluate: S(2ex - 4x) dx A. 2e*4* + C B. -2ex + 4x + C 4x C. 2ex + C In 4 4x D. 2e* + + C In 4…

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Q: Question Suppose a population of fruit flies increases at a rate of g(t) = 4e0.11, in flies per day.…

A: Given Population of fruits flies increases at a rate of gt=4e0.1t,per dayinitial population =380…

Q: 1. A certain ellipse is centered at the origin from which the major axis is always equal to 25 and…

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: 10.1.16 Question Help w a Given parametric equations and parameter intervals for the motion of a…

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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

Q: T/6 3 coss 3x dx

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Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

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Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 2.

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Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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Q: Evaluate the double integral that will find the volume of a solid bounded by z = 4 − x^2 − 4y^2 and…

A: Let's find volume of solid.

Q: 2. Determine whether each of the following series converges or diverges. 5n - 2n (2) Σ 3n+4n n=0 +∞o…

A: Given

Q: Evaluation. 1. Determine the antiderivative for each. Show complete solution. √ 5x³=3 dx 2. √(√x√x +…

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Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: The gradient of a curve is dy/dx + (x^2)/2 = 3x. Find the equation of the curve if it passes through…

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Q: z²√(-z² + 1)5 dz

A: