Answer:
R3 <= 0.083
Step-by-step explanation:
f(x)=xlnx,
The derivatives are as follows:
f'(x)=1+lnx,
f"(x)=1/x,
f"'(x)=-1/x²
f^(4)(x)=2/x³
Simialrly;
f(1) = 0,
f'(1) = 1,
f"(1) = 1,
f"'(1) = -1,
f^(4)(1) = 2
As such;
T1 = f(1) + f'(1)(x-1)
T1 = 0+1(x-1)
T1 = x - 1
T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2
T2 = 0+1(x-1)+1(x-1)^2
T2 = x-1+(x²-2x+1)/2
T2 = x²/2 - 1/2
T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3
T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3
T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)
Thus, T1(2) = 2 - 1
T1(2) = 1
T2 (2) = 2²/2 - 1/2
T2 (2) = 3/2
T2 (2) = 1.5
T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)
T3(2) = 4/3
T3(2) = 1.333
Since;
f(2) = 2 × ln(2)
f(2) = 2×0.693147 =
f(2) = 1.386294
Since;
f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).
Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,
Since;
f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2
Finally;
R3 <= |2/(4!)(2-1)^4|
R3 <= | 2 / 24× 1 |
R3 <= 1/12
R3 <= 0.083
<span>Both variables are categorical. We analyze an association through a comparison of conditional probabilities and graphically represent the data using contingency tables. Examples of categorical variables are gender and class standing.</span>
Answer:
False.
Step-by-step explanation:
Point (1, -1) is located in Quadrant 4, while point (-1, 1) is in Quadrant 2.
I hope this helps...have a great day! ❤
Hello!
As you can see, the angles we are given make up a 90 degree angle. We have the equation below.
4x=90
To solve we just divide both sides by 4.
90/4=22.5
x=22.5
I hope this helps!
Answer:
The first three terms in the sequence are -4, -2, 0
Step-by-step explanation:
In any sequence n represents the position of the term in the sequence
<u><em>Examples:</em></u>
First term ⇒ n = 1
Second term ⇒ n = 2
Fifth term ⇒ n = 5
Let us solve our question
∵ The rule of the nth term is an = 2n - 6
→ We need to find the first three terms, means n = 1, 2, 3
∵ n = 1
∴ a1 = 2(1) - 6
∴ a1 = 2 - 6
∴ a1 = -4
∴ The first term is -4
∵ n = 2
∴ a2 = 2(2) - 6
∴ a2 = 4 - 6
∴ a2 = -2
∴ The second term is -2
∵ n = 3
∴ a3 = 2(3) - 6
∴ a3 = 6 - 6
∴ a3 = 0
∴ The third term is 0
The first three terms in the sequence are -4, -2, 0
