Ek=1(-1)k-1_7 9k-1 Determine whether the series converges and if so, find its sum. O 1/2 63/8 63/10 O 1/4

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

Q: Find the first partial derivatives of the function f(x, y, z) = xz – 5x²y³z*.

A: Find the first partial derivative of function f(x,y,z)

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A: We need to prove that V is not a subspace of R3  .Below find the solution in the image.

Q: If f(x)=x, then f'(5) = (A) 0 (B) 5 (C) 1 25 (E) (D) 5

A: Topic:- derivatives   

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Q: y = Cje2" + C2e¯®

A: y=C1e2x+C2e-x differentiate with respect to x dydx=2C1e2x+(-1)C2e-xdydx=2(y-C2e-x)-C2e-xdydx=2y-2C2e...

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A: Topic = Functions

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Q: zeros of the function f(x) = 12x - 19x2 - 101x - 60. Enten ced by commas.

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Q: Evaluate the integral. (Use C for the constant of integration.) (x^2-25)^1/2/x^3 dx

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Q: Given the points G(1, –1, 3), H(-1, 2, 1), and K(4, 1, 1), find GH + GK ) × GH · ( GH + HK -23 31

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Q: /1+x-1 lim 1-0 V4 - a - v4- x2

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Q: Given that f(−5)=−10 and f′(−5)=−2, find an equation for the tangent line to the graph of y=f(x)at x...

A: Topic = Functions