Let F of x equals the integral from 1 to 3 times x of the natural logarithm of t squared. Use your calculator to find F″(1).
2 answers:
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Answer:
x = 2
Step-by-step explanation:
First, let's write out our equation:
I want to isolate x on one side, so first, I'll add 4 to both sides to remove the -4 from next to 2x:
Notice that I combined like terms with the -4 and 4 (to get 0) and the 6 and 4 on the right side (to get 10). Next, I'll add 3x to both sides:
And then I'll add like terms:
Now, all we have to do is divide both sides by 5:
And there's our answer. Hopefully that's helpful! :)
There is no common ratio or common difference. The first three terms increases more slowly than a cubic, but the last three increase more quickly than the cube of n. The pattern is not obvious to me. When the sequence is cast in recursive terms, you get
... a[n] = (48/13)a[n-2] + (59/39)a[n-1] . . . . a[1] = 2, a[2] = 9
The next term using this rule is 174 34/39, not an integer.
The coefficients p and q for a[n-2] and a[n-1] can be found from
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Any sequence of 4 numbers can be matched by a polynomial of degree 3 or less. Here, a calculator's polynomial regression function tells us the rule could be
... a[n] = 4.5n³ -24.5n² +49n -27
Using this rule, the next two terms are 168 and 357.
