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
arc length = pi /180 * angle in degree * radius
2 = pi/180 * 30 *r
2 = pi/6 *r
multiply by 6/pi
12/pi =r
3.819718634 =r
Answer: r =3.82 inches
Answer:
x = 7
Step-by-step explanation:
A, B, and C are collinear B is between A and C.
AC = AB + BC
2x + 1 = x + 4 + 2x - 10
2x + 1 = 3x - 6
2x - 3x = - 6 - 1
- x = - 7
x = 7
Answer:
ye
Step-by-step explanation:
Answer:
8 by 12 units
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is 1.5w. The perimeter is 4 more than 3 times this, so is (3(1.5w) +4) = 4.5w+4
The perimeter is given by the formula ...
P = 2(length + width)
Filling in the given values for the variables, we have ...
4.5w +4 = 2(w +1.5w)
4 = 0.5w . . . . . . subtract 4.5w and collect terms
8 = w . . . . . . . . . multiply by 2
length = 1.5×8 = 12
The rectangle is 8 units wide and 12 units long. The perimeter is 40 units.
