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Comparison Test or Limit Comparison Test
In the preceding section we saw how to relate a series to an improper integral to find out the convergence of a series. When the integral test is a good test, it does force us to do improper integrals that aren't all time easy and in some cases may be not possible to find out the convergence of.
For example consider the subsequent series.
To make use of the Integral Test we would have to integrate
∫∞0 1/ (3x + x) dx
and I'm not even make sure if it's possible to do this integral. Nicely sufficient for us there is other test that we can use on this series that will be very much easier to use.
1st, let's note that the series terms are positive. Like, with the Integral Test that will be significant in this section. Next let us note that we should have x > 0 as we are integrating on the interval 0 ≤ x < ∞. Similarly, regardless of the value of x we will all time have 3x > 0. Thus, if we drop the x from the denominator the denominator will get smaller and therefore the whole fraction will obtain larger.
Differentiate the following functions. (a) f (t ) = 4 cos -1 (t ) -10 tan -1 (t ) (b) y = √z sin -1 ( z ) Solution (a) Not much to carry out with this one other
Sir, I am a Maths teacher from kolkata,India.i want to join your website as Maths'' expert.Please guide me as to how to join your website and earn some money. I will be really grat
Solve -10 cos(3t )= 7 on [-2,5]. Solution Let's first get the inverse cosine portion of this problem taken care of. cos(3 t )= - 7/10 ⇒ 3t = cos -1 ( - 7
Characteristics and Limitations of moving average Characteristics of moving average 1) The more the number of periods in the moving average, the greater the smoothing
The Robin's Nest Nursing Home had a fundraising target of $9,500. By the end of the fundraiser, they had exceeded their goal through $2,100. How much did they raise? Exceeded
We will firstly notice the undamped case. The differential equation under this case is, mu'' + ku = F(t) It is just a non-homogeneous differential equation and we identify h
Consider the clique graph below. a) How many subgraphs of G with 3 nodes are there? b) How many of the subgraphs defined in part(a) are induced subgraphs?
52/7
i need help with exponents and how to add them
One-to-one function: A function is called one-to-one if not any two values of x produce the same y. Mathematically specking, this is the same as saying, f ( x 1 ) ≠ f ( x 2
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