Which of the following is indeterminate at x = 1? x2 +1 х2 — 1 x² – 1 x² +1 х — 1" x +2 Vx +3 – 2' Vx + 3 – 2 - -

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

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Q: 3. Use the IVT to prove that y = x ln x has at least one zero on 2'2

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Q: Find f'(x). f(x) = = O V 10x - sin²(7x) 1 f'(x) = = 2√/10 - 14cos(7x) 1 f(x) 2√10x - sin² (7x) 10…

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Q: Suppose Fas satisfies f'cx) = fex). Prove that 3fx)sin(3x) + f'cx)cos (3x) Sfewcos(3x) dx = %3D 10

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Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

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Q: 4 Find the mul hiplicity of the foll owing faunchons 3 2. a-9xt 30 L -4yx at x= 3 and x=2 3. 2. ) f-…

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Q: Which of the following has a singular point at x = 2?

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Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: lim (1 - cos(3x))sin(7x) of (c) 이이 O 0° O 100 O o. c0 O co - c0 O not indeterminate 8 %

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Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

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Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: Evaluate the following integral. cos x dx -6x 1 sin 2x dx 2 - 6n O C. dx + cos 2x dx OD. dx + - 6x 6…

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Q: (d) Show that there is some x with 0 < x < 2 such that x2 + cos(ax) = 4. %3D

A: Solution-