Chapter 5, Problem 55RE

(a)

To determine

To find: TheGraphing device to graph the function.

Answer to Problem 55RE

The function $\text{y=Cos}\left({\text{2}}^{\text{0}\text{.1x}}\right)$ is even function.

Explanation of Solution

Given: $\text{y=Cos}\left({\text{2}}^{\text{0}\text{.1x}}\right)$

Concept used:

Changes in value of doesn’t Changes the sign of the function so the function is neither even nor odd.

Its $\text{Domain=}\left(-\infty ,\infty \right)$ and $\text{Range=variable}\text{.}$

Calculation:

Thee graph of the $\text{y=Cos}\left({\text{2}}^{\text{0}\text{.1x}}\right)$ .

  

Graphing device use here is Desmos graphing calculator. from the graph modulus symbolize the positivity of the function which is shown in the graph.

Through graph range can determined which is

Range here is variable in positive direction and its constant in negative direction.

  $\text{Domain=}\left(-\infty ,\infty \right)$ .

(b)

To determine

To find:whether the Function is periodic if then described it.

Answer to Problem 55RE

The period here is non periodic.

Explanation of Solution

Given: $\text{y=Cos}\left({\text{2}}^{\text{0}\text{.1x}}\right)$

Concept used:

Period is measured as distance it takes for the entire graph to repeat.

Since the period of the Cosine function is $\text{π}$ .

Calculation:

  $\text{y=Cos}\left({\text{2}}^{\text{0}\text{.1x}}\right)$

Form the graph its clearly verified the periods as:

The period here cannot be verified since graph here changes with changes in its value so its ineither increasing nor decreasing.

Hence the period here is non periodic.

(c)

To determine

To find: The graph whether the function is even or odd.

Answer to Problem 55RE

The function is neither even nor odd.

Explanation of Solution

Given: $\text{y=Cos}\left({\text{2}}^{\text{0}\text{.1x}}\right)$

Concept used:

  $\text{f}\left(\text{-x}\right)\text{=f}\left(\text{x}\right)$ the function is an even function.

  $\text{f}\left(\text{-x}\right)\text{=-f}\left(\text{x}\right)$ the function is and odd function

Calculation:

  $\text{y=Cos}\left({\text{2}}^{\text{0}\text{.1x}}\right)$

Here the variable x doesn’t Changes the sign of the function so it’s neither even nor odd function.

  $\text{f}\left(\text{-x}\right)\ne \text{f}\left(\text{x}\right)$ and $\text{f}\left(\text{-x}\right)\text{=-f}\left(\text{x}\right)$ .

Hence function is neither even nor odd.