Notice that if
, then
. Recall the definition of the derivative of a function
at a point
:
So the value of this limit is exactly the value of the derivative of
at
.
You have
Answer:
6
Step-by-step explanation:
First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.
Expanding, we get
(x³-3x+1)² = (x³-3x+1)(x³-3x+1)
= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1
= x^6 - 6x^4 + 2x³ +9x²-6x + 1
In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots
Cancel something
we cancel x's
multiply 1st equation by 5 and 2nd by 7 and add them
-35x-30y=-5
<u>35x-28y=7 +</u>
0x-58y=2
-58y=2
divide both sides by -58
y=-1/29
sub back
5x-4(-1/29)=1
5x+4/29=1
minus 4/29 from both sides
note, 1=29/29
5x=25/29
divide bot sides by 5 (or times 1/5)
x=5/29
(5/29,-1/29)
Answer:
1) 2x^4/343
2) 2x^6/225
3) 2x^12/25
4) 5x^20/16807
Step-by-step explanation:
Hope this helps!
Yes it is greater than 1,000
