If We Approximate $\int_{1}^{\infty} \frac{1}{x^{2}+1} d x$ With $\int_{1}^{b} \frac{1}{x^{2}+1} d x$

question 1

Multiple Choice

If we approximate $\int_{1}^{\infty} \frac{1}{x^{2}+1} d x$ with $\int_{1}^{b} \frac{1}{x^{2}+1} d x$ what value of b could we use to estimate the value of $\int_{1}^{\infty} \frac{1}{x^{2}+1} d x$ with an error of less than 0.01? Of the following, select the smallest value of b that will work.

• A)50
• B)125
• C)250
• D)500

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Definitions:

Expression

In genetics, the process by which information from a gene is used to synthesize a functional product, such as protein, leading to the manifestation of a phenotype.

Pleiotropy

A genetic phenomenon where a single gene influences multiple phenotypic traits in an organism.

Seed Coat Color

The external color of a seed's protective outer layer, which can vary based on species and genetic factors.

Susceptibility

The likelihood or predisposition of an individual or population to be affected by a disease or condition based on genetic or environmental factors.