Answer:
To Prove:
is equal to the sum of its Maclaurin series.
Step-by-step explanation:
If
, then
for all n. If d is any positive number and |x| ≤ d, then
So Taylor's Inequality, with a = 0 and M =
, says that
Notice that the same constant
works for every value of n.
But, since
,
We have 
It follows from the Squeeze Theorem that
and therefore
for all values of x.

By this theorem above,
is equal to the sum of its Maclaurin series, that is,
for all x.
Answer:
f(x)= x^3-5x^2-23x-12
Step-by-step explanation:
Given:
function f(x) divided by x + 2, the quotient is x2 – 7x – 9 and the
remainder is 6
When a polynomial f(x) is divided by any another polynomial d(x) and there is q(x) and r then it can be written as:
f(x)= d(x)q(x) + r
Now putting values of d(x)= x+2, q(x)= x2 – 7x – 9 and r=6, we get
f(x)= (x+2)(x^2-7x-9)+6
f(x)= x^3 -7x^2-9x+2x^2-14x-18+6
= x^3-5x^2-23x-12 !
Let's call the amount of money they still need "x". So far they have 425 dollars and they require more than $950. So the inequality is...
425 + x > 950
x > 950 - 425
x > 525
They still need to raise more than $525
The answer for this equation is x=3
Answer:
<u>The multiples of 3 are:</u>
These the 3 out of 10 results.
<u>The probability of selecting a multiple of 3 is:</u>
- P = 3/10 as fraction
- = 0.3 as decimal
- = 30% as percent