Find the limit of {4sqrt3-(cosx+sinx)^5}/(1-sin2x) as x approaches to pi/4?

Question

#{4sqrt3-(cosx+sinx)^5}/(1-sin2x)#

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Answer 1 · 2017-12-15T14:29:26

Please see below

#lim_(xrarr pi/4) (4sqrt3-(cosx+sinx)^5)/(1-sin2x) # has form
#(4sqrt3-(sqrt2/2 + sqrt2/2)^5)/(1-1)^+ = (4sqrt3-(sqrt2)^5)/0^+#

# = (4sqrt3-4sqrt2)/0^+#

So the limit does not exist because as #xrarrpi/4#, #f(x)# increases without bound.

#lim_(xrarr pi/4) (4sqrt3-(cosx+sinx)^5)/(1-sin2x) = oo#.