Q2 TF - Calculus

Question

what is the limit of comparison test for improper integrals?

Step-by-Step Solution

Answer

if f and g are continuous ,positive functions for all values of x and .

then 1) if $0<k<\infty$then ${\int }_a^{\infty }g\left(x\right)dx$ converges then  ${\int }_a^{\infty }f\left(x\right)dx$converges.

2) if k=0 then ${\int }_a^{\infty }g\left(x\right)dx$ converges then${\int }_a^{\infty }f\left(x\right)dx$ converges.

3) if k=$\infty$then ${\int }_a^{\infty }g\left(x\right)dx$ converge then${\int }_a^{\infty }f\left(x\right)dx$ converges.

Step 1: Understand the Question

We are asked:
what is the limit of comparison test for improper integrals?

Step 2: Recall the Definition

We recall the relevant mathematical definition or concept.

Step 3: State the Answer

if f and g are continuous ,positive functions for all values of x and . then 1) if 0 < k < ∞ then ∫ a ∞ g ( x ) d x converges then ∫ a ∞ f ( x ) d x converges. 2) if k=0 then ∫ a ∞ g ( x ) d x converges then ∫ a ∞ f ( x ) d x converges. 3) if k= ∞ then ∫ a ∞ g ( x ) d x converge then ∫ a ∞ f ( x ) d x converges.