Use taylor's theorem with integral remainder and the mean-value theorem for integrals to deduce taylor's theorem with lagrange remainder

As consequence of the Taylor theorem with integral remainder we have that

If we ask that has continuous th derivative we can apply the mean value theorem for integrals. Then, there exists between and such that

Hence,

Thus,

and the Taylor theorem with Lagrange remainder is

.

Step-by-step explanation:

step-by-step explanation:

given perimeter: 28cm

length: 9cm

atp,

2(l+w)=p of the reactangle

2(9+x)=28

18+2x=28

2x=28-18

x=10/2

x=5

therefore width is 5 cm