Find the minimum speed of a particle with trajectory c(t) = (t3 – 4t, t2 + 1) for t > 0. Hint: it is easier to find the minimum of the square of the speed.

Q: Find curl (8z i + 9x j+ 10y k). curl (8z i + 9x j+ 10y k) (i )i + ( i j + ( )k

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Q: S cos³ 3x dx

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Q: Evaluate the definite integral. i+e'j+t k )dt ell (e-l – 1) + (ell – 1) i – (e-1 – 1) j +, k 11 ell…

A: Given: I=∫01e11t i+e-t j+t kdt   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2).…

A: Solving

Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: 8 Evelluate the double integral: + 3x) dydx

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Q: View Policies Current Attempt in Progress Find r'(t). r(t) = (tan-(9t))i+t cos(t)j – Vik | NOTE:…

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Q: dy for x'e*y Find dx sin' ( 3x) + In (y) by using implicit differentiation.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: You and your best friend Janine decide to play a game. You are in a land of make believe where you…

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Q: 31) Find two sets af poler Coorelinates for tue pornt (0,-4) Jer OLQL2T Auywers's 37 テノ, (16,…

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Q: 11. Let -4 А -4 -4 -3 -3 (a) (i) Show that -4 is an eigenvalue of A with corresponding eigenvector…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: Determine the vactor feld of F. F(z, y) = yi - j

A: This is a problem related to vector field calculation. Based on the general concept we will provide…

Q: Evaluate the definite integral. ellt i+ej+t k)dt O ell – 1 (e – 1) + (ell – 1) i – (e-l – 1) j + k…

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Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

Q: Determine the radius and interval of convergence of the following power series. The radius of…

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Q: Determine if the following series converge: 2.4.6 . · (2n) ... (a) (b) ) Inn 3.6 - 9 · · · (3n) ...…

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Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

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Q: 2. Use the limit theorems to find the following limit. x2 – 5x – 14 lim x→7 x - 7

A: Given :limx→7x2-5x-14x-7

Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Find y=f(x), if f''(x)=3x^2, f'(0)=-7 and f(0)=2.

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Q: dx 5-x?

A: We will solve the integral.

Q: The graphs of f(x) and g(x) are shown. For what values of x does f(x) = g(x)? x = -2, x = 0, x = 3…

A: We have to choose correct option

Q: Problem 4. The third term of a geometric sequence is 9, and the common ratio is 2 Find the fifth…

A: Given :3rd tern of GP is 9common ratio=32

Q: fsin 3xcos3xdx 19.

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question...…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: This question can be solved using the concept of domain and of functions and value of a function at…

Q: Problem 3. at a speed of 60 cm/s. Suppose the function g models the radius as a function of time t…

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Q: dx ²+8x-9

A: Given: ∫dxx2+8x−9 Let I = ∫dxx2+8x−9 ⇒I = ∫dxx2+9x-x−9

Q: tdt 1-t4

A: Topic = Integration

Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x² – 9…

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Q: 12. The demand function for 66 piece Tinkertoy set is D(q) 750 and the supply q+1 function for…

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Q: 2x dx e 2X-1

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Q: S V25 – 4x²

A: For the solution follow the next step.

Q: Q2) Find the integral of: 6 tan*x dx

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Q: dx x?(4x++9)Z

A: Integration are simplyfied..

Q: dr Let A be the area of a circle with radius r. If dt dA = 2, find dt when r = 5.

A: Given :drdt=2r=5

Q: ; Test the following series whether it is convergent or divergent (show all your works) n2 +7 a) 2…

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Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: 8) Fiad the volume of the solid gonereted by revelving the regien beunded by tue graphs of equetians…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the graphs…

Q: Find the second and third derivative of the function (a) f(x) = x6 – 3.x5 – 41x – 73 - |

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Q: f is just that e*-sin(x + y) + cos(x +y)] and = -e* sin(x + y) which if the ollowing is true Select…

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Q: Evaluate the definite Integral. Use a graphing utility to vertfy your result. dx Step 1 To evaluate…

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Q: the comverg ence and divergene test 2n

A: To find the convergence of the series.

Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: Integration

A: We will solve the integral.

Q: In ASTR, t = 15 ft, r = 16 ft, mLS = 35°. Find the area of the triangle and round to the nearest…

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Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula k(t) to find k(t). 13 r(t) = 10 cos(7t)i+ 10 sin(7t)j+…

A: Given; r(t)=10cos(7t)i+10sin(10t)j+3tk

Q: り (2xy+y?) dx - 2x? dy = o 2) Yy dx - (メ+ 2y)? dy -0

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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