## Trending News

Promoted

# Limit question, why can't Mathway answer it?

Why can't mathway answer this???

Limit (sqrt(0.25x^2+1)-1)/(0.5x)

x → inf

### 1 Answer

Relevance

- kbLv 78 years agoFavorite Answer
lim(x→∞) [√(0.25x^2 + 1) - 1]/(0.5x)

= lim(x→∞) [√(0.25x^2 + 1) - 1] * [(√(0.25x^2 + 1) + 1] / {0.5x [(√(0.25x^2 + 1) + 1]} via conjugates

= lim(x→∞) [(0.25x^2 + 1) - 1] / {0.5x [(√(0.25x^2 + 1) + 1]}

= lim(x→∞) 0.5x / [(√(0.25x^2 + 1) + 1].

Now, divide each term by x = √x^2:

lim(x→∞) 0.5 / [(√(0.25 + 1/x^2) + 1/x]

= 0.5 / [(√(0.25 + 0) + 0]

= 1.

I hope this helps!

Still have questions? Get your answers by asking now.