C h e c k space w h e t h e r space t h e space l i m i t space e x i s t space f o r space f left parenthesis x right parenthesis equals e to the power of open vertical bar x close vertical bar end exponent space a t space x equals 0

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Asked by Topperlearning User | 16th Nov, 2016, 01:11: AM

Expert Answer:

e to the power of open vertical bar x close vertical bar end exponent equals e to the power of x space f o r space x greater or equal than 0
space space space space space space space space space space space e to the power of negative x end exponent space f o r space x less than 0
F o r space t h e space l i m i t space t o space e x i s t space a t space x equals 0 space t h e space l e f t space h a n d space l i m i t space m u s t space b e space e q u a l space t o space r i g h t space h a n d space l i m i t.
L e f t space h a n d space l i m i t equals
limit as x rightwards arrow 0 to the power of minus of e to the power of open vertical bar x close vertical bar end exponent
equals limit as x rightwards arrow 0 to the power of minus of e to the power of negative x end exponent
equals limit as h rightwards arrow 0 of e to the power of negative left parenthesis 0 minus h right parenthesis end exponent
equals limit as h rightwards arrow 0 of e to the power of h equals 1
R i g h t space h a n d space l i m i t equals
limit as x rightwards arrow 0 to the power of plus of e to the power of open vertical bar x close vertical bar end exponent
equals limit as x rightwards arrow 0 to the power of plus of e to the power of x
equals limit as h rightwards arrow 0 of e to the power of left parenthesis 0 plus h right parenthesis end exponent
equals limit as h rightwards arrow 0 of e to the power of h equals 1
L H L equals R H L thin space s o space t h e space l i m i t space e x i s t s space a t space x equals 0

Answered by  | 16th Nov, 2016, 03:11: AM