How do you do this question?

Step-by-step explanation:

f(x) = ln(1+2x), a = 5, n = 3

Find the derivatives.

f⁽⁰⁾(5) = ln(1+2(5)) = ln(11)

f⁽¹⁾(5) = 2 / (1+2(5)) = 2/11

f⁽²⁾(5) = -4 / (1 + 2(5))² = -4/121

f⁽³⁾(5) = 16 / (1 + 2(5))³ = 16/1331

T₃(x) = ln(11) (x − 5)⁰ / 0! + 2/11 (x − 5)¹ / 1! − 4/121 (x − 5)² / 2! + 16/1331 (x − 5)³ / 3!

T₃(x) = ln(11) + 2/11 (x − 5) − 2/121 (x − 5)² − 8/3993 (x − 5)³

Find the fourth derivative.

f⁽⁴⁾(x) = -96 / (1 + 2x)⁴

So the next term of the series would be:

(-96 / (1 + 2x)⁴) (x − 5)⁴ / 4!

For 4.6 ≤ x ≤ 5.4,│f⁽⁴⁾(x)│is a maximum at x = 4.6.  Therefore:

│R₃(x)│≤ │(-96 / (1 + 2(4.6))⁴) (4.6 − 5)⁴ / 4!│

│R₃(x)│≤ 0.000009

│R₃(x)│is always positive, so we can ignore the right two graphs.  Only the top left graph is less than 9×10⁻⁶ on the interval.

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!