iv) x₂ = (1 + √2/2)4n²¸

Q: 2°3 а.

A: Every power series converges over a certain open interval. This interval is determined by the ratio…

Q: Q2 Prove that the scries 2+ x2 3+X2 4+x is Unitormly convergem? in any interval?

A: The given series is: 11+x2+12+x2+13+x2+……. Therefore the given series can be written as:…

Q: What is the continuous extension?

A:

Q: n=1 7+4rn

A: The given series diverges.

Q: What is the Continuous Extension to a Point?

A: A function has the intermediate value property if and only if whenever function satisfies the two…

Q: 10i Defermin Hhe radins of convereonce of the folloming sevies. Then test the endpints to de fermime…

A:

Q: n+1 Σ()" n=0 (x + 2)"

A: We have to determine the interval of convergence for the power series

Q: Based on the table,  If M(x)=f(g(x)), then M'(1)=

A: Given: To determine: M'1

Q: Determine If the divergent FoIOLWng intergral is convergent and find its value· or S. i

A:

Q: (x + 2)" Determine the interval of convergence of 3n +1 n=1

A:

Q: In your own words, explain why the divergence test is inconclusive when the limit of the sequence is…

A: Divergence test tests for divergence, not convergence.

Q: QuApplyany appropriate test fr comergence or 00 12+3n 2n-7 n=1

A: For series ∑an to be convergent necessary condition is limn→∞an=0 Given series is : ∑an=∑2+3n2n-7…

Q: Using the definition of uniformly convergence, determine if the or not uniformly in the interval:…

A:

Q: For golden section method and newton's method ,how far away from a minimum can be tested if without…

A: Given: Here, How far away from a minimum may be tested using the golden section method and Newton's…

Q: Let fn be a bounded sequence of functions uniformly convergetn to f. Prove that f is bounded as…

A:

Q: 1. Use one of the comparison tests to determine if the serics converges or diverges: Ssin? k k2 k=1…

A:

Q: Is the fo llowing mtegral conuergent or divergent ?

A:

Q: est the couvergence or divergence

A:

Q: 1. Evaluate using Determine the open disk of convergence and radius of convergence of 2 3 a.

A:

Q: (ii) Find the pointwise limit of the sequence. (iii) Show that the convergence is uniform on any…

A: note : As per the instruction we will only solve the part (ii), (iii) of question 1

Q: tind the interval and radias of convergence for n(x-4)" n3+1 c)

A:

Q: Explain the theorem about liner and superlinear convergence?

A:

Q: How can we further classify superlinear convergence?

A: As per the question we have to classify the superliner convergence mathematically with proper…

Q: (-1)"+12na" n² + 3 V. Determine the interval of convergence of

A:

Q: Determine the interval and radius of convergence.

A: