Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 11 sin(t)j + 9tk; t = NOTE: Enter the exact, simplified answers. K =

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Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

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A: answer is in next step . as per guideline i can only answer one question

Q: Find the arc length L of the graph of r(t). r() = r° i + 1 j+Vor k, 3 <t<7 L = i

A: Given problem:-

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Q: The following differential equation is exact. Find the general solution. (7x + 6y) dx + (6x − 8y3)…

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A: Given :

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Q: A farmer finds that if she plants 85 trees per acre, each tree will yield 65 bushels of fruit. She…

A: answer is in next step

Q: L3a²dx = 65 %3D Select one: O True O False

A: We have to find out integration

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Q: Use a graph of g to estimate lim g(x) or to show that the limit does not exist. Evaluate g(x) near x…

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Q: x+1 1.

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Q: es conve n=1

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Q: SIL- W : x² + y} < 9, 0<z<6

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve).…

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

A: We have to find the inflection point and the concavity and convexity of the curve

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), Y = e' sin(t), z =…

A: Given;  x=etcost, y=etsint, z=11et.

Q: Which of the following is an antiderivative of f(x) = 12x³ - 9x2 + 8x – 3?

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Q: Find out whether the series given below converges or diverges. 00 In (n+ 1) Σ n+1 n= 1 Choose the…

A: Here we will find whether series is convergent or divergent,

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Q: t Attempt in Progress antity P is an exponential function of time t, such that P = 40 when t = 4 and…

A: for simplicity take P0=a Given  for t=4 , P=40 for t = 3 , P = 50

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Q: nd the volume of the solid generated by

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Q: f(1) 100 g(x) lim where f(r) and g(x) are seen in the graph.

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Q: Find for the parametric curve c(t) (t-1 – 5t, 41) at the point t = -2. dx (Use symbolic notation and…

A: Given problem:- Find dy/dt for the parametric curve c(t) = (t-1 - 5t, 4t3) at the point t = −2.

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Q: The height h, in meters, of an object at time t is given by 12t + 18t – 6t2 .h(t) What is the height…

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Q: An antiderivative for is: 22 +81+20 1 O In + C I+8 ㅇ 올tan-1 () +C 금i미플의 O In 28|+ C O tsec- (4) + C

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Q: At the beginning, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: let weight is exponential growth function

Q: Evaluate F. dr. Jc F(x, y) = 9xi + 6yj C: r(t) = ti + V4 - tj, -1 sts 1

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Q: Solve using Gauss-Jordan elimination. 4x1 - 7x2 - 5x3 = 41 X1 - 3x2 = 14 Write the system of…

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Q: csc?y dy is equal to A -у соty — coty dy B) None у сoty — coty dy D у сoty + coty dy

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Q: Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 1 1 + 8 1 + +... p =…

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Q: Evaluate the integral. dx (x – 4)(x – 7) - (Use symbolic notation and fractions where needed. Use C…

A: Solving the problem by finding the value of integral.

Q: 4. Evaluate •5 (4 – 2.x) dx - 2,

A: topic - definite integral

Q: One of the correct. steps to evaluate x²inx. x²Inx dx to yield the correct integral (A dx x2Inx B x³…

A: The given integral,     ∫x2lnx dx

Q: Find the volume of the solid that is bounded by the surfaces z = = 92 - x2 - y2 in the first octant.…

A: 0≤ z ≤ 81-x2-y2z=0x2+y2=920≤y≤81-x20≤x≤9

Q: Use the substitution u = x° + 8x to find the following indefinite integral. Check your answer by…

A: Use the substitution method to solve the integral.

Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

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Q: A cylindrical can is being filled at the rate of at =3t" , h(t) describes the height of the…

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Q: 4- The graph of f is given in the figure to the right. Let A(x) = | f(t) dt and evaluate A(4), A(6),…

A: Integration gives area under curve  area above x axis is positive  area under x axis is negative.

Q: 00 (n+7)! Does the series converge or diverge? 7!n!7" n= 1 Choose the correct answer below. O A. The…

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Q: Complete parts a through c for the given function. f(x) = 4x° - 5x - 40x° + 5 on [- 3,4] c. Identify…

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Q: Find the Jacobian d(x, y) / d(u, v) for the indicated change of variables. u- v), y =u + v) X = -

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