Question

Find the values of y = c(x) = for x = 0, 0.008, 0.027, 0.064, 0.125, 0.216, 0.343, 0.512, , 0.729, and 1.

Answer 1

c(x) is a function, then we will solve the problem for two different functions.

1. If
`c(x)=(x)/(0.5)+x`

Then

`y=c(x)`

`y=(x)/(0.5)+x`

Using each of the values for x we have.

When x=0 the result is:
`y=(0)/(0.5)+0=0`

When x=0.008 the result is:
`y=(0.008)/(0.5)+0.008=0.016+0.008=0.024`

When x=0.027 the result is:
`y=(0.027)/(0.5)+0.027=0.054+0.027=0.081`

When x=0.064 the result is:
`y=(0.064)/(0.5)+0.064=0.128+0.064=0.192`

When x=0.125 the result is:
`y=(0.125)/(0.5)+0.125=0.25+0.125=0.375`

When x=0.216 the result is:
`y=(0.216)/(0.5)+0.216=0.432+0.216=0.648`

When x=0.343 the result is:
`y=(0.343)/(0.5)+0.343=0.686+0.343=1.029`

When x=0.512 the result is:
`y=(0.512)/(0.5)+0.512=1.024+0.512=1.536`

When x=0.729 the result is:
`y=(0.729)/(0.5)+0.729=1.458+0.729=2.187`

When x=1 the result is:
`y=(1)/(0.5)+1=2+1=3`

2. If
`c(x)=sin(x)+2x`

Then

`y=c(x)`

`y=sin(x)+2x`

Using each of the values for x we have.

When x=0 the result is:
`y=sin(0)+2(0)=0`

When x=0.008 the result is:
`y=sin(0.008)+2(0.008)=0.000139+0.016=0.016139`

When x=0.027 the result is:
`y=sin(0.027)+2(0.027)=0.000471+0.054=0.054471`

When x=0.064 the result is:
`y=sin(0.064)+2(0.064)=0.001117+0.128=0.129117`

When x=0.125 the result is:
`y=sin(0.125)+2(0.125)=0.002182+0.25=0.252182`

When x=0.216 the result is:
`y=sin(0.216)+2(0.216)=0.003769+0.432=0.435769`

When x=0.343 the result is:
`y=sin(0.343)+2(0.343)=0.005986+0.686=0.691986`

When x=0.512 the result is:
`y=sin(0.512)+2(0.512)=0.008936+1.024=1.032936`

When x=0.729 the result is:
`y=sin(0.729)+2(0.729)=0.012723+1.458=1.470723`

When x=1 the result is:
`y=sin(1)+2(1)=0.017452+2=2.017452`