The series ∞ (-10) k k! k=1 is an alternating series but we can apply the ratio test to ∞ (-10) k k! to test for absolute convergence. Applying the ratio test for absolute convergence you would compute ak+1 lim k→∞ ak = lim = k→∞ Hence the series converges

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A: Answer is in step 2.

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A: we have to find sine function.

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A: This question can be solved using the concept of inverse Laplace transform.

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A: Given : A value that a function approaches the output for the given input values Here, it has been…

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Q: x²-3x - 7 √(x² + x + 2) (2x - 1) dx

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Q: 4. Use cylindrical coordinates to evaluate [!] √²³² + y²dv₁ D where D is the region that lies inside…

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Q: [18x² √6x³ +5 dx 3 ○a. — (6׳ +5)³/4 + C b. (6x³ +54/5 + Oc.5(6x³+5)¹/5 + C d. 5 Od (6x³+5) ³/4 + C…

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A: Given the query is to find the best fit function.

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A: close allclear allformatclc A = 21;B = 5;C = 3;y1 = @(x) B * sin(A*pi*x) .* cos(x);y2 = @(x) B *…

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Q: 3t AT(1) The temperature T of a person during an illness is given by T(t) = +98.6, where T is the…

A: T(t)=3tt2+3+98.6A)T'(t)=(t2+3)ddt(3t)-3t…

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Q: Find the limit. lim (t i − 3 j + t² k) 1-5 lim (t i − 3 j + t² k) − i 1-5 i k = i+ i j+

A: We can find the exact answer as below

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Q: 38. a10-49.5, a14 = -73.5

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Q: 9- Give five examples about application of polar coordinates in real life

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A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

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A: Solve for the f(x)

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A: We can differentiate the function as below.

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Q: Can you draw it please

A: We first write y in terms of x. x230+y216=1y216=1-x230y2=161-x230y=±161-x230

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Q: 2. Find a power series solution of the differential equation y' = 4y

A: To find a power series solution of the following differential equation.y'=4y

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A: Integration by parts formula:∫u.v=u∫v-∫u'∫v