find the approximation of the function (x^3-2x^2x^2x-1)/(x^2+2x+1)
(x^3-2x^2x^2x-1) is it
x³-2x⁵-1???
No limit was given as well
and again
I don't know how you would
Approximate this rather than simplifying it
(x^3-2x^2x^2x-1)/(x^2+2x+1)
that middle term in the numerator makes no sense, a typo?
we could divide by x^2
= (x - ?? - 1/x^2)/(1 + 2/x + 1/x^2)
To find the approximation of the given function, we can perform polynomial long division.
Step 1: Write the given function in descending order of powers of x:
f(x) = (x^3 - 2x^2x^2x - 1)/(x^2 + 2x + 1)
Step 2: Divide the highest power term of the numerator by the highest power term of the denominator to get the first term of the quotient. In this case, the quotient term is x.
x * (x^2 + 2x + 1) = x^3 + 2x^2 + x
Step 3: Subtract this term from the numerator, and bring down the next term:
(x^3 - 2x^2x^2x - 1) - (x^3 + 2x^2 + x) = -2x^2x^2x - 2x^2 - x - 1
Step 4: Repeat steps 2 and 3 until there is no remainder left.
The next step will be to divide the highest power term of the current numerator (-2x^2x^2x) by the highest power term of the denominator (x^2). This will give the next term of the quotient: -2x^2.
-2x^2 * (x^2 + 2x + 1) = -2x^4 - 4x^3 - 2x^2
Subtract this term from the numerator:
(-2x^2x^2x - 2x^2) - (-2x^4 - 4x^3 - 2x^2) = -2x^4 - 4x^3
Bringing down the next term:
-2x^4 - 4x^3 - (0) = -2x^4 - 4x^3
Now we have no terms with degree higher than x^2 in the current numerator, so we stop.
Step 5: Write the final quotient:
The quotient we obtained so far is:
x - 2x^2
This is the approximation of the given function.