Pre-calc limit help: Given E= (mc^2)/((1-(v^2/c^2))^0.5), find E as v->0

[pf1996]

the energy of an object with mass [FONT=MathJax_Math-italic]m[/FONT] and velocity [FONT=MathJax_Math-italic]v[/FONT] is given by the equation, where c is the speed of light:

E= (mc^2)/((1-(v^2/c^2))^0.5)

question 1: Find the energy in the limit that the velocity goes to zero.
question 2:What happens to the energy as the velocity [FONT=MathJax_Math-italic]v[/FONT] approaches the speed of light, [FONT=MathJax_Math-italic]c[/FONT]?

I'm really lost on the idea of limits, and how they are going to be used in calculus. This question confuses me even more, especially question 1. Any insight would be helpful.

 

[tkhunny]

the energy of an object with mass [FONT=MathJax_Math-italic]m[/FONT] and velocity [FONT=MathJax_Math-italic]v[/FONT] is given by the equation, where c is the speed of light:

E= (mc^2)/((1-(v^2/c^2))^0.5)

question 1: Find the energy in the limit that the velocity goes to zero.
question 2:What happens to the energy as the velocity [FONT=MathJax_Math-italic]v[/FONT] approaches the speed of light, [FONT=MathJax_Math-italic]c[/FONT]?

I'm really lost on the idea of limits, and how they are going to be used in calculus. This question confuses me even more, especially question 1. Any insight would be helpful.

Limits constitute the fundamental concept that made the calculus possible! You are wise to spend time understanding limits.

Q1: What happens to the value of E as v gets small? c and m are constants. 2 and 1 and 0.5 are constants.
What happens to v/c as v gets small (or "goes to zero" or "approaches zero" or "vanishes")?
What happens to v^2 / c^2 as v gets small?
What happens to 1 - v^2 / c^2 as v gets small?
What happens to (1 - v^2 / c^2)^0.5 as v gets small?
Your task is to analyze the behavior on the approach.
It is a common error to believe your task is to state what happens when you ARE there. We are ONLY approaching, NOT arriving. In some cases, these are the same, but let's not assume that from the start.