3 years ago

If anyone knows this please help me. Please answer only if you know. Thanks! more points for you if answered!

1 answer:

3 0

1a) Possible rational roots will be of the form
±{divisor of 10}/{divisor of 4}
Divisors of 10 are {1, 2, 5, 10}
Divisors of 4 are {1, 2, 4}

Then possible rational roots are
{±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10}

1b) Your answer is correct.

2) One additional root will be the conjuate of the given complex root.
5 -3i

3) If one root is 5 -√7, another will be 5 +√7. Then your polynomial is
P(x) = (x -(5 -√7))*(x -(5 +√7)) = (x -5)^2 -(√7)^2
P(x) = x^2 -10x +18

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G evaluate lim h → 0 (1 + h)9 − 1 h . hint: this limit represents the derivative of a function f at a given point

Bond [772]

$\displaystyle\lim_{h\to0}\frac{(1+h)^9-1}h$

Write $1=1^9$ , and recall that for a differentiable function $f(x)$ , the derivative at a point $x=a$ is given by

$f'(a)=\displaystyle\lim_{h\to0}\frac{f(a+h)-f(a)}h$

which would suggest that for this limit, $f(x)=x^9$ and $a=1$ . We have $f'(x)=9x^8$ , and so the value of the limit would be $9(1)^8=9$ .