Evaluate $\lim _ { x \rightarrow - 2 } ( x + 1 ) ^ { 5 } \sqrt { 2 x ^ { 4 } + x ^ { 2 } }$

question 45

Essay

Evaluate $\lim _ { x \rightarrow - 2 } ( x + 1 ) ^ { 5 } \sqrt { 2 x ^ { 4 } + x ^ { 2 } }$ , and justify each step by indicating the appropriate Limit Law(s).

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Definitions:

Variance

A measure of the dispersion of a set of data points around their mean; the square of the standard deviation.

Level of Significance

The probability threshold below which the null hypothesis is rejected in hypothesis testing, typically denoted by alpha (α).

Null Hypothesis

A statement that there is no effect or no difference, and it serves as the default or starting assumption in hypothesis testing.

Variance

A measure of the dispersion of a set of data points around their mean value, quantifying how much the data points differ from each other.