11,16,21,... Find the 43rd term. Find the 43rd term.
1 answer:
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Answer:
Step-by-step explanation:
<em>The </em><em>Remainder Theorem</em><em> states that when you divide a polynomial by a linear factor
, where
is a constant, the remainder is
evaluated at
</em>
<em>Moreover, according to the </em><em>Factor Theorem</em><em>, an extension of the Remainder Theorem, if the remainder of the function is </em><em>0</em><em> when evaluated at
, then
is said to be a factor of the polynomial
</em>
Given the 2 theorems above, it follows that if is a factor of
, then the remainder is equal to 0 when
is evaluated at
Which means
Third answer choice is correct.
Answer:
a) integral = 24.72
b) |Error| ≤ 0.4267
Step-by-step explanation:
a)
The integral:
can be approximated with the midpoint rule, as follows:
6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72
(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)
b)The error bound for the midpoint rule with <em>n</em> points is:
|Error| ≤ K*(b - a)^3/(24*n^2)
where <em>b</em> and are the limits of integration of the integral and K = max |f''(x)|
Given that -5 ≤ f''(x) ≤ 1, then K = 5. Replacing into the equation:
|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267