For the limit below, find values of δ that correspond to the M values.?
lim (tan(x))^2 = infinity
x-->pi/2
M-------> 500 and 5000
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lim (tan(x))^2 = infinity
x-->pi/2
M-------> 500 and 5000
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Verified answer
We need to find δ such that |x - pi/2| < δ ==> |tan^2(x)| > M.
Solve for M:
tan^2(x) > M
==> |tan x| > sqrt(M)
==> |x| > Arctan(sqrt(M)).
So, let δ = pi/2 - Arctan(sqrt(M)). (since pi/2 > Arctan(sqrt(M)).)
I hope that helps!