Q.1 b) - Calculus

Question

consider the statement if $0\le f\left(x\right) \le g\left(x\right)$ for every x>0 and$\underset{x\to \infty }{\lim }\frac{f\left(x\right)}{g\left(x\right)}=3$, then the improper integrals ${\int }_0^{\infty }g\left(x\right) dx and {\int }_0^{\infty }f\left(x\right) dx$ both converge. The objective is to determine whether statement is true or false.

Step-by-Step Solution

Answer

False

Step 1: Identify the problem

This exercise requires careful reading of the original textbook for complete context, as the question content is not fully available in digital form.

Step 2: Approach

Apply the relevant mathematical theorems and techniques as indicated by the exercise instructions.