Q1-) Determine whether the following functions are convergent or divergent: 1 1- En=1 ((3n-1)*/ cos2n

Q: sin N 8) Show that converges/diverges.

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Q: Let the function g be defined by g(x) = (x^6 + 2)/7. Use the Fixed-Point Theorem to show that the…

A: This question is basically based on the theorem named Banach fixed point Theorem which states that:…

Q: WNII sin 2 7) Show that 4 VN converges/diverges.

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Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

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Q: Determine if converge or diverge using nth term and if converge find its limit

A: Finally, we can say that : The sequence an​=(−1)nn+1n​ diverges.The sequence an​=4n3n+n​​…

Q: 3. (a) Let an max{sin 1, sin 2, sin 3,... sin n} Does {an} converge? What is its limit? Explain. =

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Q: Examine the convergence of ,where a>1. (log x)" +1

A: First I have told about Improper integral of first kind and then using it evaluate the given…

Q: „(4 - 1) = "p : И

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Q: dx Study the convergence of 1= Solution

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Q: (-1)"-1 (In n)" 00 23. E n=2

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Q: Let Xn=nn for n EN * Show that Xn+₁ <Xn if and only if (1+1)^<N. *Show that the inequality is valid…

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Q: 3. A particle moving along the x-axis has velocity function v(t) = t²e-t. How far does the particle…

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Q: 1. determine if it diverges or converges n e2n n=1

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Q: (c) By working out the second smallest positive solution to the equation Sg x² 29y² = ±1, compute…

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Q: 9. Determine whether the following is convergent or divergent +(-1)"+1 n! 2n 2e

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Q: 24.6 Let fn(x) = (x − 1)² for x = [0, 1]. (a) Does the sequence (fn) converge pointwise on the set…

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Q: 00 +8 dx converges. Perform a test to determine if - 00 x° +8 Does dx converge or diverge? .9 1…

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Q: If 2 Cnx" is convergent when x=2 and divergent when x=-3, then 2 Cn is n=0 n =0 convergent. O…

A: Consider the given information: The series ∑n=0∞Cnxn is convergent when x=2 and divergent when x=-3.…

Q: Let W be the region in the figure bounded by the cylinder x² + y² = 8, the plane z = x + 2, and the…

A: Let a vector field F→ be continuous partial differentiable.S is the closed boundary surface of a…

Q: 9) n+3"

A: Comparison test for series of positive terms states that, If an, bn are two series such that…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.