Question

find the limit and confirm your answer using the Sandwich Theorem as the lim x approaches positive and negative infinity 1-cos x/ x^2

Answer 1

follow me?

Answer 2

can you explain what you just did?

Answer 3

cosx is varing -1 to 1

Answer 4

its value is varing -1 to 1 dependent on x value

Answer 5

so -1<cosx<1 and if you take negative sign all parts then -1<-cosx<1

Answer 6

and add each part 1 then 0<1-cosx<2 and devide each part as x^2

because x^2 is always positive, 0<(1-cosx)/x^2<2/x^2

Answer 7

finally take limitation x goes to infinity then you can get 0<lim[(1-cosx)/x^2<0

Answer 8

Thank you!