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
S.A = (2×area of base) + area of lateral faces
Area of lateral faces = area of base × height
Area of lateral faces = 19×4×8=608
S.A = (2×19×4)+608
=760
Answer:
x = 23
Step-by-step explanation:
AE = EC
so, 5x + 3 = 118
5x + 3 = 118
Bring +3 to the other side so -3
5x = 118 - 3
5x = 115
Bring 5 to the other side so:
x = 115 ÷ 5
x = 65
Answer:
v = - 5
Step-by-step explanation:
Given
- 18 = 5v + 7 ( subtract 7 from both sides )
- 25 = 5v ( divide both sides by 5 )
- 5 = v
Answer:
To find volume of a tent this would be your formula:
start by taking the base of the triangle on your tent typically located in the front
1/2 (height) (width) to get your area (DONT SKIP THIS STEP)
Then take your area you just calculated and do
(area) (length)
Let me give you an example:
in the picture below
height: 3 cm
length: 8 cm
Width: 12 cm
Next do your first formula:
1/2 (3)(12)= 18 cm
(Calculation of one face)
then your second:
(18)(8)= 144 
Hopefully this guide helped you sorry i couldn't answer your question without a picture!
