Use definitions (rather than limit theorems) to prove the following limit exists. Identify the limit. Lim as X approaches -1 from the right of 1/(x^2-1 ).

I need help by October 28th at around 1pm. This is an advanced calculus 1 problem. I am having a hard time using definitions instead of limit theorems that I'm used to.

In your own words, define multivariate analysis. Name the most important factors contributing to the increased application of techniques for multivariate data analysis in the last decade. List and describe the multivariate data analysis techniques described in this chapter. Cite examples for which each technique is appropriate. Explain why and how the various multivariate methods can be viewed as a family of techniques.FULL SCREEN PRINTER VERSION BACK NEXT question G A population has a distribution that is skewed to the left. Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample mean of size , = 26. The central limit theorem can be applied. The central limit theorem cannot be applied. airlyExercise 7 Suppose Y = (Y1,Y2, . . . , Yn)' follows a multivariate normal distribution with EG'Z) = ,u, var] = 02, and that the covariance matrix of Y can be expressed as E = 02V, where V is n x n symmetric matrix of known constants. Obtain explicit expressions for the maximum likelihood estimators t. and 6'2 of 9 = (,u, oar. Consider the sequence {an} dened by an 2 1/4732 + 1m 2n. \"=1 (1) Use the Main Limit Theorem to prove that this sequence converges. Please point out which part of this theorem you use each time you invoke it, taking care to justify why you can apply it. Hint: As it is written, convince yourself that you cannot naively apply the Main Limit Theorem to {a}ff'=1. (2) Using only the definition of what it means for a sequence to converge, prove that this sequence converges to the h'rnit you determined above. (3) Write a. few words describing your appreciation for the Main Limit Theorem