Answer:
-1.5
Step-by-step explanation:
3/8 is 0.375 in decimal form
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
Answer:
A) 
Step-by-step explanation:
![f(n) = \sqrt[3]{n} -2](https://tex.z-dn.net/?f=f%28n%29%20%3D%20%5Csqrt%5B3%5D%7Bn%7D%20-2)
![y = \sqrt[3]{n} -2](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7Bn%7D%20-2)
Hope this helps!
Answer:
The answer is (d) ⇒ eccentricity = 6 , hyperbola , directrix x = 3/2
Step-by-step explanation:
∵ r = ek/(1 ± ecosФ)
∵ r = 9/(1 + 6cosФ)
∴ e = 6 ⇒ eccentricity = 6
∵ e > 1
∴ The conic is hyperbola
∵ ek = 9
∴ k = 9/6 = 3/2
∴ The directrix x = 3/2
