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How do you know if a series converges by the intergral test?
When you take the integral using the series as integrand, it converges if the integral worked out to be a number. If it's infinte, the series diverge.
What properties of a function can be discovered from its Maclaurin series?
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
What is a sequence that converges to 0 but the series diverges?
harmonic series 1/n .
What are the different rules of finding the limit of function?
Given a function sequence f1(x), f2(x), f3(x)..., the limit can be defined in several ways: - Point by point limit; that is, it converges to a new function at each point. - Lp convergence; that is, it converges to a new function in Lp-norm. - Almost everywhere convergent; that is, it converges to a new function except a set with measure zero.
What is the function of spectacle?
it converges light into a specific point of our eye so that we can see the object clearer.
