What is the value of the limit xycos xySolutionlet xyt you n

Solution

let xy=t

you need to find

lim(t->0)[t/cos(t)]

write the series for cos(t)

cos(t) = 1 - (t²/2) + (t⁴/24) +...........

so the expression [t/cos(t)] becomes

[t/(1 - t²/2 + t⁴/24 +...........)]

put t = 0 in above expression in denominator all terms except 1 become 0,

the entire expression becomes,

[0/(1-0)] = (0/1) = 0

hence

lim(xy->0)[xy/cos(xy)] = 0

hope you got it