1 Σ 2n + 1) ! Find the radius of convergence for n=0 1 Solution: Set Then %3D 1)! 2n + 1 |a,| 1 |an+1| 1 Jan| R = lim n→0 an+1 lim 1 lim lim ||

Q: a' + b' + c\!/r 9" - Vabe. Geometric mean Prove that lim 3 where a, b, and c are positive real…

A: Let Take natural logarithm on both sides.

Q: Find the limit

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Q: Prove that the family of all polynomials of degree < N with co- efficients in (-1, 1] is uniformly…

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Q: Compute 4n — бп? lim Vlan| for a,n %3D 3n2 +7 n-00

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Q: Evalvate the limit Tet fGa) =2x²+8 fl4+h)-f(4) lim

A: Consider the given function, fx=2x2+8 to find value of fh+4 substitute x=4+h and to find value of f4…

Q: 4. Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for n≥ 1, we have 1ª +…

A:

Q: 4) A coin is dropped from a height of 960 feet. The height, s (measured in feet), at time, t…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 3) Show that the functions max: R" R. (₁,...,n) max(₁,....n) and min: R" → R. (₁.) → min(x₁,....)…

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Q: Vx* +5x' +3 dx x' +2x? +4

A: Given that, ∫1∞x5 + 5x2 + 3x3 + 2x2 + 4dx To test the convergence/divergence of the function We can…

Q: Let f(x) = 3x² + 13x + 12 3x² + 7x + 2 This function has: 1) Vertical asymptotes at x = 2)…

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Q: 3 Prove that bim li a) b) lin (√√m² + +1 M-) D (√√√²+1 -√₂)=0 nti M-) D 2 ·m) = a -

A: By rationalisation