Let r(t) = t²i + t cos(πt)j + sin(ät) k, find ſª r(t) dt.

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A: A detailed solution is given below.

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A: Please see the below picture for detailed solution.

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A: We have to solve given Questions.

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Q: If the following equality is known to be true: -Ax + B x²2x-3 5 dx = -= √, ²2²3 - 2²/₁1 x - x + What…

A: Given data:- ∫-Ax+Bx2-2x-3dx=∫2x-3-5x+1dx

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A: Volume of a circular cylinder is V=πr2h

Q: Find the explicit solution of the initial value problem: dy dt 3 4ty+y y(1) = -5

A: We can find the solution as below.

Q: Q 14) Does the sequence converge or diverge. If it​ converges, find the limit.

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A: Given:          r=3+2cosθ , r=2

Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

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Q: n=1 n! n - (x − 3)" 2n

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A: Given: The point P (1, -7,1) and the line r (t ) = <3 − 2t, 4t, 7> . So,             x = 3 −…

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A: I am attaching image so that you understand each and every step.

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A: We have to find the area of given function.

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Q: Calculus

A: Please refer to the image below

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A: The region is bounded by the curves y=ln x and y=ln2x from x=1 to x=2

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A: find the integration?

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Q: 2x3 2x² + 3 3 Submit an exact answer using fractions if needed. Find the average value of f(x)…

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Q: 3. Explain why lim √2x - 6 does not exist.

A: 3. The given limit is limx→32x-6 Note:    Multiple questions are given, we are answer with only one…

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: 3. Find the Taylor polynomial of degree 3 centered at x = 4 for the function defined by f(x)=√x.…

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Q: If R = {(x, y) : 0 ≤ x ≤ 1,0 ≤ y ≤ 1}, then find (²+1) +2 0 1 arctan O 2√2 3 0 √2 3 O √2 3 (√³/₂2)…

A: Please see the below picture for detailed solution.

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