calculus ab/bc - 6.3 riemann sums. sum (rectangles) on the interval a, b. what is the width of each sub…
calculus ab/bc - 6.3 riemann sums. sum (rectangles) on the interval a, b. what is the width of each sub - interval (rectangle)? δx = (b - a)/n. 1. if n is approaching infinity, whats the width approaching? b a ∞ 0
Answer
Explanation:
Step1: Recall width formula
The width of each sub - interval in a Riemann sum is given by $\Delta x=\frac{b - a}{n}$.
Step2: Analyze limit as n approaches infinity
We want to find $\lim_{n\rightarrow\infty}\Delta x=\lim_{n\rightarrow\infty}\frac{b - a}{n}$. Since $b - a$ is a constant, and we know that $\lim_{n\rightarrow\infty}\frac{c}{n}=0$ for any constant $c$. Here $c = b - a$, so $\lim_{n\rightarrow\infty}\frac{b - a}{n}=0$.
Answer:
0