Over which interval are the exponential and linear function approximately the same? from 0.25 to 0.5 from 0.5 to 0.75 from 0.75
2 answers:
Answer:
Answer is 0.25 to 0.5
Step-by-step explanation:
Let the linear function be
and exponential function be
x 0.25 0.5 0.75 1.0 1.25 1.5
y 0.25 0.5 0.75 1.0 1.25 1.5
Diff 0.25 0.25 0.25 0.25 0.25
e^x 1.29 1.65 2.12 2.72 3.49 4.48
Diff 0.36 0.47 0.60 0.77 0.99
Hence 0.36 to be nearer to 0.25, than other intervals
So answer is 0.25 to 0.5
You might be interested in
Answer:
Step-by-step explanation:
Given the series,
∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)
So,
∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞
There are different types of test to show if a series converges or diverges
So, using Ratio test
Lim n → ∞ (a_n+1 / a_n)
Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))
Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))
Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)
Lim n→ ∞ (-1/2)^(n-n+1)
Lim n→ ∞ (-1/2)^1 = -1/2
Since the limit is less than 0, then, the series converge...
Sum to infinity
Using geometric progression formula
S∞ = a / 1 - r
Where
a is first term
r is common ratio
So, first term is
a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1
a_1 = -4
Common ratio r = a_2 / a_1
a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2
a_2 = 2
Then,
r = a_2 / a_1 = 2 / -4 = -½
S∞ = -4 / 1--½
S∞ = -4 / 1 + ½
S∞ = -4 / 3/2 = -4 × 2 / 3
S∞ = -8 / 3 = -2⅔
The sum to infinity is -2.67 or -2⅔
Check attachment for better understanding
The given ratio of the sides of the triangles is 4:10:7. Let the sides be 4x, 10x and 7x .
And given perimeter is 252 meters .
Perimeter is the sum of all sides. So we get
Dividing both sides by 21
So the sides are