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.
Answer:
-8 < x< 3
Step-by-step explanation:
|2x+5| <11
there are two solutions, one positive and one negative ( remember to flip the inequality for the negative)
2x+5 <11 and 2x+5 > -11
Subtract 5 from each side
2x+5-5 < 11-5 and 2x+5-5 > -11-5
2x< 6 and 2x>-16
Divide by 2
2x/2 <6/2 and 2x/2 >-16/2
x <3 and x>-8
-8 < x< 3
x is less than 3 and x is greater than -8
open circles and -8 and 3 and a line between
Answer:
X=7-3y
is the equation formed here
Answer: 708$ approximately.
Step-by-step explanation:
There is 12 months every year so 34,000 divided by 12. So she makes about 2,833 a month. Then about 4 weeks per month so you divide 2833 by 4 and it’s 708$ per week.
