Chapter 14, Problem 40RE

(a)

To determine

To graph: The function $f(x$

  $f\left(x\right)=2x+3$)=2x+3 .

Explanation of Solution

Given: on interval $\left[0,4\right]$

The given function is $f\left(x\right)=2x+3$ .

This is linear function. Graph this function on $\left[0,4\right]$ .

  

(b)

To determine

To graph: The four sub-interval of equal length and choose left end points of each sub-interval.

Explanation of Solution

Given: $f\left(x\right)=2x+3$ on interval $\left[0,4\right]$

Make partition in graph into four subintervals of equal length and choose u as the left end point of each sub interval.

  

(c)

To determine

To graph: The four sub-interval of equal length and choose right end points of each sub-interval.

Explanation of Solution

Given: $f\left(x\right)=2x+3$ on interval $\left[0,4\right]$

Make partition in graph into four subintervals of equal length and choose u as the right end point of each sub interval.

  

(d)

To determine

To graph: The eight sub-interval of equal length and choose left end points of each sub-interval.

Explanation of Solution

Given: $f\left(x\right)=2x+3$ on interval $\left[0,4\right]$

Make partition in graph into eight subintervals of equal length and choose u as the left end point of each sub interval.

  

(e)

To determine

To graph: The eight sub-interval of equal length and choose right end points of each sub-interval.

Explanation of Solution

Given: $f\left(x\right)=2x+3$ on interval $\left[0,4\right]$

Make partition in graph into eight subintervals of equal length and choose u as the right end point of each sub interval.

  

(e)

To determine

To find: The area of the graph.

Answer to Problem 40RE

  $28\text{ sq units}$

Explanation of Solution

Given: $f\left(x\right)=2x+3$ on interval $\left[0,4\right]$

The given graph of $f\left(x\right)=2x+3$ on interval $\left[0,4\right]$ is look like a trapezium.

Area of graph, $A=\frac{1}{2}\times 4\left(3+11\right)=28\text{ sq units}$