Write the integer represented by H. List its opposite and absolute value.
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Answer: Hello mate!
Clairaut’s Theorem says that if you have a function f(x,y) that have defined and continuous second partial derivates in (ai, bj) ∈ A
for all the elements in A, the, for all the elements on A you get:
This says that is the same taking first a partial derivate with respect to x and then a partial derivate with respect to y, that taking first the partial derivate with respect to y and after that the one with respect to x.
Now our function is u(x,y) = tan (2x + 3y), and want to verify the theorem for this, so lets see the partial derivates of u. For the derivates you could use tables, for example, using that:
and now lets derivate this with respect to y.
using that
Now if we first derivate by y, we get:
and now we derivate by x:
the mixed partial derivates are equal :)
The result of the division of polynomial <em>3.23 + 8x2 + 9x + 10</em> by <em>x + 2</em> is; 3x² + 2x +5
<h3>Long division of polynomials</h3>According to the question given;
- The result of the long division of polynomials can be evaluated as in the attached image.
By observation of the procedures in the attached image, we may conclude that the expressions (x+2) and (3x² + 2x +5) are factors of; 3x³ + 8x2 + 9x + 10
Learn more on polynomials division;
