Q9. Which of these is not the derivative of the function, y = x": A. -½x-1½ B. –0.5x-1Vx-1 C. –0.5 1 D. 2xVx - х1.5

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: Given the graph of the function f(x), answer the following question. -30 B C F -20 -10 A D E 4 -10…

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Q: For the plane curve x = 4t, y = 3t²1, where 0 ≤ t ≤ 3, the arc length is given by 3 [ f(t) dt. Find…

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Q: Calculate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: 4. A graph of a function y = f(t) is shown below. Use this graph to answer the following questions…

A: We will use If f(x) is a function. Then roots of f'(x) is called critical points and if f'(a)=0.…

Q: Find the limits. If you use L'Hopitals Rule, make sure to justify why you can use it. 1- cos(2r) lim

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Q: A 25-year-old woman burns 350 - 60t cal/hr while walking on her treadmill. Her caloric intake f…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Use the Divergence Theorem to find the flux of F(x, y, 2) = (a* – e)i+ (y³ + sin z)j + (2³ – cy)k 3…

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Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: Let f (x) = x³ 3x². - Find the absolute minimum value of f(x) on the interval [1, 4].

A: We have to find the function value

Q: 1 O Evaluate lim (3" + 7")

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Q: If 3x² + 2x + xy 2 and y(2) -7, find y' (2) by implicit differentiation.

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Q: Given that f, g, and h are functions with values f(2) = –4, g(2) = –2, and h(2) = 2, and…

A: We have to find following expression.

Q: 4. x³ dx (x²+2)³

A: We have to calculate the given indefinite integral according to the given information

Q: Consider the plane curve given by the parametric equations x = t² + 3t - 26 y = t² + 3t - 28 - What…

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Q: Identify the function, whose derivative is defined below: dy (х + h)2 — х2 lim h→0 dx h А. f(x) — Һ.…

A: Given dydx=limh→0(x+h)2-x2hWe know that the limit derivative formula is f'(x)=limh→0f(x+h)-f(x)h

Q: АВ C D E F This is a graph of f'(x), the derivative of f(x)

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: QUESTION 8 If you save $270 per quarter for retirement in an account that earns 8% interest per…

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Q: Simplify the following expression. X d * J V4+t* dt (Hint: Vi+Pt ,2 1 +t dt = + dt + dx - X -X -X

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Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

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Q: Let f(x) = x³ - 3x². Find the absolute minimum value of f(x) on the interval [1, 4].

A: The given function,  f(x)=x3-3x2 on the interval 1,4

Q: √(x + 3) dx √16-x²

A: Solution

Q: 10. Consider the system of equations X, - 2x, + 3x, = 1 2х, — Зх, — 2х, 3 3 X, - x, - 5x, = 2 a.…

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. Σ+1+1, k+5 k(k…

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Q: Suppose that a, b, and c are unknown constants such that f(x) = x² + ax + b and g(x) = e(3z–3) %3D…

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 200 + 1000t - 150t², where t…

A: To find out the numbe of cars pass through the intersection between 6 am and 11 am.

Q: Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A: To calculate ddtr1t·r2t and ddtr1t×r2t first by differentiating the product directly and then by…

Q: Find all rational zeros of the polynomial, and then find the irrational zeros, if any. Whenever…

A: Solution:

Q: Evaluate the definite Integral 4 600 St дос 2 √ 1 + 300²

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Q: √1² +25 -2 I dt

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Q: d Calculate ri(t)· r2(t)] and ri(t) × r2(t)] first by differentiating d dt dt the product directly…

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Q: c. The area between y sin x and the x – axis for 0 < x< a

A: Area between the y=sinx and x axis from x=0 to x=π

Q: B. Find the area of the region bounded by the following: 20. inside 1-² = 2 cos 20 and outside = 1

A: We need to find area of region.

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

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Q: Solve the following linear programming problem. Maximize: z = 3x+8y subject to: 6x + 5y ≤ 30 10x + y…

A: Objective function: z=3x+8y Constraints:  6x+5y≤3010x+y≤30x≥0, y≥0   Now we have to find the…

Q: Evaluate the integral of the following using Miscellaneous Substitution X Sdx 1+x 5.

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

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Q: 1. ++x xp. dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the k-component of (curl F) for the following vector field on the plane F=(x+y)i + (8xy)j

A: Solution: F=(x+y)i + (8xy)j       P             Q k-component

Q: A 25-year-old woman burns 200- 20t cal/hr while walking on her treadmill. Her caloric intake from…

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Q: f(x)= = x+1 1³ - 2x² + 1

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Q: What is the difference between a function and a parametric curve? Make sure to justify your answer.…

A: This is a problem related to function and parametric equation for the same. Based on the general…

Q: * Using the formula sin(bx)] dx = (721 ) eax [a sin(bx) – b cos(bx)] + C a² + b². |[e-8x sin(6x)] dx…

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Q: Compute the Jacobian for the change of variables given by u= x+y and v=x-y. O a.-2 O b. 1 2 O c. 1 2…

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Q: Find the limit. If you use L'Hopitals Rule, make sure to justify why you can use it. f(x) 40 g(x)…

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Q: Find the indefınite integral and check the result by differentiation. Find the antiderivative whose…

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

A: The idea of ratio test must be there to understand it properly. The explanation part is given below.