prove this quantity (1-x^2/2)<=cosx<= (1-x^2/2)+(x^4/4*3*2)
Remember that the values of cosine function are included in the interval [-1;1].
You must show that the inequality is true.
`1- (x^2/2) =lt cos x = lt 1- (x^2/2) + x^4/24`
Add the quantity `x^2/2` to the left and to the right of inequality, to keep it stable.
`1- (x^2/2)+ (x^2/2)=lt cos x = lt 1- (x^2/2) + (x^2/2) +x^4/24`
Yo may reduce the opposite terms:
`1=lt cos x = lt 1+x^4/24`
Notice that the left side is a false statement because the values of the cosine function do not overpass 1.
ANSWER: The inequality is not true.