Some symbols are missing. I'm assuming you meant to put in a horseshoe symbol like so
If so, then the contrapositive of that would be
which is the final answer.
The tilde sign
means "not" so writing
means "not q" which is the complete opposite of q.
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: -1/3
Step-by-step explanation:
The formula is y2 - y1/ x2 - x1 . So the answer would be -1/3 bc 3 - 2 = 1 and -11 - (-8) = -3.
Because the ratio of acceptance is 9:100, we simply multiply both by 2:
9:100 = 18:100
The chances of her admitting the 18th student is Option B., 100%
