Use the definition of a taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (enter your answers as a comma-separated list.) f(x) = 7 1 + x , a = 2

The first four nonzero terms of the Taylor series of around are:

Step-by-step explanation:

The Taylor series of the function f at a (or about a or centered at a) is given by

To find the first four nonzero terms of the Taylor series of around you must:

In our case,

So, what we need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.

Evaluate the function at the point:

Evaluate the function at the point:

Evaluate the function at the point:

Evaluate the function at the point:

Evaluate the function at the point:

Apply the Taylor series definition:

The first four nonzero terms of the Taylor series of around are:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is