Answer:
-x¹⁴ / 5040
-½ < x < ½
Step-by-step explanation:
f(x) = e^(-x²)
The Taylor series for eˣ centered at 0 is:
eˣ = ∑ (1/n!) xⁿ
Substitute -x²:
e^(-x²) = ∑ (1/n!) (-x²)ⁿ
e^(-x²) = ∑ (1/n!) (-1)ⁿ x²ⁿ
The 14th degree term occurs at n=7.
(1/7!) (-1)⁷ x¹⁴
-x¹⁴ / 5040
ln(1 + x) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ xⁿ / n
If we substitute 4x²:
ln(1 + 4x²) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ (4x²)ⁿ / n
Using ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺² (4x²)ⁿ⁺¹ / (n+1)] / [(-1)ⁿ⁺¹ (4x²)ⁿ / n]│< 1
lim(n→∞)│-1 (4x²) n / (n+1)│< 1
4x² < 1
x² < ¼
-½ < x < ½
Answer
4. - x ^ 2 + 13x - 42 <= 0524211r
5. x ^ 2 - 11x - 42 < 0
16 - x ^ 2 + 9x - 8 <= 0
17. x^ 2 -11x+80<0
18. - x ^ 2 + 3x + 4 <= 0
19. x ^ 2 - 12x + 36 <= 0
20. 2x ^ 2 - 32x + 56 < 0
21. x ^ 2 - 10x - 96 < 0
Answer:
5. 57 9. 63
Step-by-step explanation:
Im Smart
It’s cheaper to take this bus. Compare 166 to 190
Answer:
She spent 8 dollars.
Step-by-step explanation:
24 divided by 3 is 8