Chapter B.1, Problem 10E

(a)

To determine

Whether the given expression $\frac{1}{x+3}=O\left(\frac{1}{x}\right)$ is true or false.

(b)

To determine

Whether the given expression $\frac{1}{x}+\frac{1}{x^2}=O\left(\frac{1}{x}\right)$ is true or false.

(c)

To determine

Whether the given expression $\frac{1}{x}-\frac{1}{x^2}=o\left(\frac{1}{x}\right)$ is true or false.

(d)

To determine

Whether the given expression $2+\cos x=O\left(2\right)$ is true or false.

(e)

To determine

Whether the given expression $e^x+x=O\left(e^x\right)$ is true or false.

(f)

To determine

Whether the given expression $x\ln x=o\left(x^2\right)$ is true or false.

(g)

To determine

Whether the given expression $ln\left(\ln x\right)=O\left(\ln x\right)$ is true or false.

(h)

To determine

Whether the given expression $\ln \left(x\right)=o\left(\ln \left(x^2+1\right)\right)$ is true or false.