# lim cos2x - 1/cosx - 1

Evaluate : limx-0  cos2x -1/cosx-1

=limx-0  (2cos2x -1) -1/cosx-1
=limx-0  (2cos2x -2)/cosx-1
=limx-0  2{(cos2x -1)}/cosx-1
=limx-0  2 {(cosx -1)(cosx+1)} /cosx-1
=limx-0  2 {(cosx -1) (cosx+1)} /(cosx-1)
=limx-0  2 {(cosx +1)}
Applying the Limit :
=2 {(cos0 +1)}
=2 {(1 +1)}
=4

limh-0  cos2x -1/cosx-1 = 4

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limx1[x-2/x2-x-1/x3-3x2+2x]
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1/(x+a)(x+b)(x+c)
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Evaluate :?limx-0??cos2x -1/cosx-1

=limx-0??(2cos2x -1) -1/cosx-1

=limx-0??(2cos2x -2)/cosx-1

=limx-0??2{(cos2x -1)}/cosx-1

=limx-0??2 {(cosx -1)(cosx+1)} /cosx-1

=limx-0??2 {(cosx -1) (cosx+1)} /(cosx-1)

=limx-0??2 {(cosx +1)}

?Applying the Limit :

=2 {(cos0 +1)}

=2 {(1 +1)}

=4

limh-0??cos2x -1/cosx-1 =?4
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Find

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Lim cos2x-1/cosx-1
=Lim (1-2sin?x)-1/cosx-1
=Lim -2sin?x/cosx-1
=Lim -2(1-cos?x)/cosx-1
=Lim -2(1-cos?x)/-(1-cosx)
=Lim 2(1+cosx)(1-cosx)/(1-cosx)
=Lim 2(1+cosx)
Now putting X=0 we get,
=2?2. [ As cos0=1]
=4
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