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Mathematics

1 answer:

valentina_108 [34]2 years ago

3 0

Answer:

x =1 for the first problem

and for second question

Step-by-step explanation:

Let's solve your inequality step-by-step.

|2x+5|>0.5

Solve Absolute Value.

|2x+5|>0.5

We know either2x+5>0.5or2x+5<−0.5

2x+5>0.5(Possibility 1)

2x+5−5>0.5−5(Subtract 5 from both sides)

2x>−4.5

2x2>−4.52(Divide both sides by 2)

x>−2.25

2x+5<−0.5(Possibility 2)

2x+5−5<−0.5−5(Subtract 5 from both sides)

2x<−5.5

2x2<−5.52(Divide both sides by 2)

x<−2.75

Answer:

x>−2.25 or x<−2.75

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I need help with part b. I feel like there’s a catch, I want to do the first derivative test, however, I feel like there is a be

Sladkaya [172]

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:

$P_5(x)=g(-1)+g'(-1)\,(x+1)+g"(-1)\, \frac{(x+1)^2}{2!} +g^{(3)}(-1)\, \frac{(x+1)^3}{3!} + g^{(4)}(-1)\, \frac{(x+1)^4}{4!} +g^{(5)}(-1)\, \frac{(x+1)^5}{5!}$

and when you do its derivative:

1) the constant term renders zero,

2) the following term (term of order 1, the linear term) renders: $g'(-1)\,(1)$ 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: $g'(-1)= 7$ as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1