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:

eduard2 years ago

7 0

Reading that as

$F(x)=\displaystyle\int_1^{3x}(\ln t)^2\,\mathrm dt$

By the fundamental theorem of calculus, the first derivative is

$F'(x)=3(\ln(3x))^2$

and so the second derivative would be

$F''(x)=\dfrac{6\ln(3x)}x$

which means

$F''(1)=6\ln3$

Sindrei [870]2 years ago

5 0

Answer: answer is 6

Step-by-step explanation:

Took the test and got it correct !

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I really need help with this since I have a math test tomorrow, I'd really appreciate it if someone could help.

Elza [17]

Ok first of all, I EXTREMELY appreciate your use of parenthesis. Ok so first just raise both sides to the power of 1/2.

$(\frac{3}{8})^{x}=\frac{8}{11}$

You'll see why I didn't include a negative. Then apply the log base 3/8 and you get

$x = log_{ \frac{3}{8} }( \frac{8}{11} )$
Then you split the log up and you get
$x = log_{ \frac{3}{8} }(8) - log_{ \frac{3}{8} }(11)$
You couldn't put a negative value for a log. That is why I excluded the negative part of the sqrt.

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2 years ago

Tell whether (-9,2) is a solution of x+3y≥-2

jok3333 [9.3K]

Step-by-step explanation:

<u>Substitute the point (-9, 2) into the inequality:</u>

$-9+3(2)\geq 2$