Point form: (2,3) and x=2 and y=3
Let p(x) be a polynomial, and suppose that a is any real
number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial
long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x –
2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number
such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| <
1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2
+ x − 2| < ε/40 · 40 = ε.
Well, we can really show our work because their is no work to be done. Question 7 is a right angle because it is exactly 90 degrees. So since you now know what a right angle is, you can probably guess Question 8 a would be either 3 o'clock or 9 o'clock. For question 8b , he first one, and acute angle is an angle where it is below 90 degrees. So an example of an acute time is 3:05. An obtuse angle is an angle above 90 degrees. So an obtuse time would be (for example) 3:55. Hope this helped.
The first one, decreasing then increasing
Answer:
12
Step-by-step explanation:
Therefore, the answer is 12.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
