Math for fun#2, i want a to get e

TL;DR

Find the value of 'a' in the power limit as X approaches infinity, (X + a) / (X - a) ^ X = e.

Transcript

let's do some math for fun and this is the power limit in calculus we are going to find a so that the limit as X approaches infinity parenthesis X plus a over X minus a and then raised to the X power this is equal to e that's special number E and in this case you know a has to be just a real number namely it has to be finite okay hmm so how can we ... Read More

Key Insights

• ☺️ The power limit equation (X + a) / (X - a) ^ X = e is analyzed using long division and substitutions.
• 🦖 By substituting T for X - a and taking the limit as T approaches infinity, the equation can be simplified to (1 + 2a) / (1 + 2a) ^ X = e.

Questions & Answers

Q: What is the equation being analyzed in the video?

The equation being analyzed is (X + a) / (X - a) ^ X = e, where the goal is to find the value of 'a'.

Q: How does the presenter simplify the equation using long division?

The presenter applies long division to the equation (X + a) / (X - a) to get 1 + 2a / (X - a), which simplifies the equation.

Q: How does the presenter substitute a variable to further simplify the equation?

The presenter substitutes the variable T for X - a, allowing them to rewrite the equation as (1 + 2a) / (1 + 2a) ^ X, simplifying the expression.

Q: How does the presenter determine the value of 'a'?

By taking the limit as T approaches infinity and setting it equal to e, the presenter deduces that 'a' must be equal to one-half.

Summary & Key Takeaways

• The video discusses finding the value of 'a' in a power limit equation as X approaches infinity.

• The equation is (X + a) / (X - a) ^ X = e.

• The presenter uses long division and substitution to simplify the equation to (1 + 2a) / (1 + 2a) ^ X, and sets it equal to 'e'.