Answer:
Step-by-step explanation:
In this system we have the force of the spring and the gravitational force. The equation that describes that is
where y0 is the equilibrium position when the string is free and y0+y is the new equilibrium position when the object is hanged of the string. By replacing by derivatives we have
the solution for this differential equation is (by using the characterisic polynomial)
hope this helps!!
Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:
and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders: since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1
Answer:
Step-by-step explanation:
Let's look at the prime factors of 210.
210 = 2 * 3 * 5 * 7
Since no factor appears more than once, this radical cannot be simplified.