1) let f(x) be a function with the following properties: i. f(0)=1
ii. For all integers n >= 0, the nth derivative, f^(n)(x)=(-1)^(n)a^(n)f(x), where a > 0 & a doesnt equal 0, in terms of a
A) write the first fur non zero terms and the general term of the power series of f(x) centered at zero, in terms of a

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

Which best describes the strength of the correlation, and what is true about the causation between the variables? it is a weak negative correlation, and it is not likely causal. it is a weak negative correlation, and it is likely causal. it is a strong negative correlation, and it is not likely causal. it is a strong negative correlation, and it is likely causal.

Select all of the quadrants that the parabola whose equation is y=√x-4 (principal square root) occupies. i ii iii iv