Evaluate:limx→0ex-esinxx-sinx A)-1; B)0; C)1; D)None of these

Linda Norman

Linda Norman

Answered

2022-12-25

Evaluate:limx0ex-esinxx-sinx
A)-1;
B)0;
C)1;
D)None of these

Answer & Explanation

Ioriannis4v

Ioriannis4v

Expert

2022-12-26Added 11 answers

The correct answer is C 1
Explanation for the correct answer:
Applying the limits and reducing the equation to its simplest form:
limx0ex-esinxx-sinxlimx0ex-esinxcosx1-cosxDifferentiatinglimx0ex-esinx-sinx+esinxcosx·cosx0--sinxDifferentiatinglimx0ex+esinx.sinx-cos2x·xesinxsinxlimx0ex+esinxcosx+sinx·esinx-cos2x·esinxcosx-2cosx-sinxesinxcosxDifferentiating
Applying the limits
e0+e0×1+0·e0·1-12·e0·1-2·1-0e011+1-11
Thus, limx0ex-esinxx-sinx=1
Option (C) is, thus, the right response.

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