One way to capture the domain of integration is with the set

Then we can write the double integral as the iterated integral

Compute the integral with respect to
.

Compute the remaining integral.

We could also swap the order of integration variables by writing

and

and this would have led to the same result.


Answer is 30
you can use PEMDAS to help you on further questions like this
P-Parenthesis
E-Exponents
M/D-Multiplication/Division solved in order from left to right
A/S-Addition/Subttaction solved in order from left to right
Answer: The quotient is 5.5
Step-by-step explanation
I believe the given limit is
![\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto%5Cinfty%7D%20%5Cbigg%28%5Csqrt%5B3%5D%7B3x%5E3%2B3x%5E2%2Bx-1%7D%20-%20%5Csqrt%5B3%5D%7B3x%5E3-x%5E2%2B1%7D%5Cbigg%29)
Let

Now rewrite the expression as a difference of cubes:

Then

The limit is then equivalent to

From each remaining cube root expression, remove the cubic terms:



Now that we see each term in the denominator has a factor of <em>x</em> ², we can eliminate it :


As <em>x</em> goes to infinity, each of the 1/<em>x</em> ⁿ terms converge to 0, leaving us with the overall limit,

Answer:
90
Step-by-step explanation:
g(-10) = (-10)²+(-10)
= 100-10 = 90