2. Give an example of an unbounded sequence {an} of negative terms such that an does not diverge to -oo.

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Q: #2. Please explain answers

A: Given:

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Q: 1. • If r + 1| < o, prove that |r³ + 1| < 0.331.

A: Here we use the fact  | x |&lt; a implies  -a&lt; x &lt; a .

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A: n1=n2=12α=0.05

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Q: 43. (-1)"ne 2n 8.

A:

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Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: c an sin d an = n (1 +(-1)")

A: As given by the question There are given that the sequences: an=sinnπ4 Now, From the properties of…

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A: Introduction :

Q: 8. If sin x- cos x = 3, find sin x sec x

A: given: sinx-cosx=13 to find: sinxsecx

Q: Suppose p is a prime and a and k are positive integers. Prove: If plak, then pk|ak.

A: Suppose p is prime. Let a and k are positive integers. If p|ak then we need to prove that pk|ak.

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Q: Give an example of a nonzero continuous function f on [0,1] such that f f(x) dx = 0.

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A: topic - quadratic equation

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A:

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