Evaluate `lim_(xto0) (1-cos(1-cosx))/(x^(4)).`

1.	Evaluate `lim_(xto0) (1-cos(1-cosx))/(x^(4)).`
Answer» `1-cos(1-cosx)=2sin^(2)((1-cosx)/(2))` `=2sin^(2)("sin"^(2)(x)/(2))` `:. underset(xto0)lim(1-cos(1-cosx))/(x^(4))=underset(xto0)lim(2sin^(2)("sin"^(2)(x)/(2)))/(x^(4))` `=underset(xto0)lim(2sin^(2)("sin"^(2)(x)/(2)))/(("sin"^(2)(x)/(2))^(2)).("sin"^(4)(x)/(2))/(((x)/(2))^(4).16)=1/8`

Discussion

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