Infinite limits and limits at infinity
See why ١x٢ grows huge near zero, draw a horizontal asymptote, and open up the forms ∞ ÷ ∞ and ∞ − ∞.
- سوريا: الصف ١١
- فلسطين: الصف ١١
- إيران: الصف ١٢
- أفغانستان: الصف ١٢
- روسيا: الصف ١٠
- ألمانيا: الصف ١١
- فرنسا: الصف ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
If f(x) grows without bound as x comes close to a number, we write limf(x) = ∞. There is no limit as a number, but the notation describes what happens; the graph has a vertical مقارب there.
When x itself gets larger and larger, the limit can be a number: lim(x→∞)f(x) = L. Then the line y = L is a horizontal مقارب.
∞ ÷ ∞ and ∞ − ∞ are not numbers; they only say there is still work to do. For a fraction of polynomials divide by the highest power of x; for a difference of roots multiply by the conjugate.