Answer:
closer look :(
Step-by-step explanation:
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
If Monica walks
1km...........................15min
?km............................60min
60/15=4
Monica walks 4km in 60 min(1H)
1km=1,000m
4km=4,000m in 1 hour
9514 1404 393
Answer:
(b) (-5, 1)
(c) (5, -7)
(d) (9, -2)
Step-by-step explanation:
The coordinate differences between the given points are ...
(4, 2) -(0, -3) = (4, 5)
The length of the line segment between the points is √(4² +5²) = √41, so this is the side of the square, not a diagonal.
The other four points that could be corners of the square are these same distances, but at right angles. To get points at right angles, the distance values can be swapped, and one of them negated.
Two of the points could be ...
(4, 2) ± (5, -4) = (9, -2) or (-1, 6)
and the other two could be ...
(0, -3) ± (5, -4) = (5, -7) or (-5, 1)
Answer:
x=15
Step-by-step explanation:
crown plz