Cos(88°) can be estimated using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2. The degrees need to be converted to radians, and by substituting into the polynomial, the cosine value to five decimal places is approximately 0.03490.
To estimate cos(88°) using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2, we first need to convert 88 degrees to radians as cos(x) expects x in radians. 88 degrees is roughly 1.53589 radians. Now, substituting x = 1.53589 into the Taylor polynomial yields the estimate.
The given Taylor polynomial is represented as cos(x) = - (x - π/2) + 1/6 * (x - π/2)³. Substituting x with 1.53589, we get:
cos(1.53589) = - (1.53589 - π/2) + 1/6 * (1.53589 - π/2)³
To get the estimate correct to five decimal places, you calculate the above expression to get roughly 0.03490. Therefore, cos(88°) is approximately 0.03490.
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First, we convert the given angle 88° into radians, since standard trigonometrical functions take angles in radians. We then substitute this into the Taylor series given, keeping in mind the importance of the remainder term.
This problem deals with the concept of Taylor series approximation, which is a widely used method in mathematics to estimate the value of functions. The given Taylor polynomial approximates the cosine function. To estimate cos(88°), we first need to convert the angle from degrees to radians, because the standard trigonometric functions in mathematics take input in radians. Remember that 180° equals π radians. So 88° can be represented as (88/180)π radians.
Substitute this into the provided series − x − π/2 + 1/6 * (x − π/2)³ + R3(x). Be wary of the remainder term R3(x). This term ensures the correctness of the approximation on the interval of convergence. The closer x is to the center, the more accurate the approximation. In practical computations, you might need to take more terms into account to ensure sufficient accuracy to five decimal places in this case.
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Answer:
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Step-by-step explanation:8 days
This is what she/he is saying:
A stone is thrown into a pool of calm water which creates concentric waves that increase the radius over time. When the external wave reaches a radius of 3 meters, it increases at a speed of 5 cm / s, at what speed does this area of the circle increase by said wave?
Answer: 90/8=11.25
Step-by-step explanation:
Answer:
R = ∞
I = (-∞, ∞)
Step-by-step explanation:
Use the ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] / [xⁿ⁺⁵ / (2n!]│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] × (2n! / xⁿ⁺⁵)│
lim(n→∞)│x 2n! / (2(n+1)!)│
lim(n→∞)│n! / (n+1)!││x│
lim(n→∞) (1 / (n+1))│x│
0
The series converges if the limit is less than 1.
The limit is always less than 1, so the radius of convergence is infinite.
So the interval of convergence is (-∞, ∞).
Answer:
it is an integer! yes ik u know that but most teachers want it to be in the smallest group u can put it in but other than that it is a real number and it is rational! A whole number is a number that is a counting number like 0,1,2,3 a natural number is a whole number without 0 like 1,2,3 a irrational number is a number that is a repeating decimal which this number isn't
If this is correct please mark me as the brainiest
Step-by-step explanation: