Select the correct relationship between ϵ \epsilon ϵ and δ δ δ to prove lim ⁡ x → 0 ( 5 x 2 ) = 0 {\displaystyle\lim_{x\to0}}\left(5x^2\right)=0 using the ε − δ ε-δ ε − δ definition of a limit.

δ = ϵ 5 \delta=\sqrt{\frac{\epsilon}{5}}

δ = ϵ 2 5 \delta=\frac{\epsilon^2}{5}

δ = ϵ 5 \delta=\frac{\epsilon}{5}

Introduction to Limits

1. Limits and Continuity / Introduction to Limits / Problem 5

Problem 5

Select the correct relationship between $\epsilon$ and $δ$ to prove $\lim_{x \to 0} (5 x^{2}) = 0$ using the $ε-δ$ definition of a limit.

$δ = \frac{ϵ^{2}}{5}$

$δ = \sqrt{ϵ}$

$δ = \frac{ϵ}{5}$

$δ = \sqrt{\frac{ϵ}{5}}$