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Ex_ 3.1. Determine, when possible; the function f(z) to which the following sequences converge in pointwise way:sin(nx) (ii ) n+23n (iii) 1+32nn+z2n (iv) n"(vi...

Question

Ex_ 3.1. Determine, when possible; the function f(z) to which the following sequences converge in pointwise way:sin(nx) (ii ) n+23n (iii) 1+32nn+z2n (iv) n"(vi) Vx

Ex_ 3.1. Determine, when possible; the function f(z) to which the following sequences converge in pointwise way: sin(nx) (ii ) n +23n (iii) 1+32n n+z2n (iv) n" (vi) Vx



Answers

In Exercises $15-26,$ use Theorem I to determine the limit of the sequence or state that the sequence diverges.
$$
z_{n}=\left(\frac{1}{3}\right)^{n}
$$

So did your father leave it? The excursion Infinite day night. Our acts on was the audition exponential function. So again, this living here goes to infinity, which divergent Bainbridge.

Limit off the anger's to infinity fire and minus 21 bedroom. And last night, so inevitable, Dickerson, we noticed under maximum power on the tongue will be about one year cancer, the maximum about in the plaque amounts of one. So we were going to do that on the factor, the maximum balance our side toe affected. And since I'm gonna five minus one other and here we have the end outside well, plus night. And so, by doing that, we can trust each other and other I am and that we have never done in it. And this to Infinity Fi minus one over. And if I mean but through our plus nine on the night. And really when Angus you infinitives and goes Jews are I'm so this unjust user, us well. And we have never only the five imam withdrawn

Okay, So by fear, um, one, we're gonna say the limit as X approaches infinity off. That's divided by the square root of X cube plus one dividing both in numerator and denominator with X to the power of three. Over two. We end up with the limit as X approaches infinity off one over the square root of ax, divided by the square root of one plus one over X cubed. This is equal this term. Uh, then goes to zero on this chairman goes to zero, so have zeroed, but one which is equal to zero.


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