Question
Asked Dec 21, 2019
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The signum (or sign) function, denoted by sgn, is defined by
if x < 0
if x = 0.
-1
sgn x =
if x > 0
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The signum (or sign) function, denoted by sgn, is defined by if x < 0 if x = 0. -1 sgn x = if x > 0

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(b) Find each of the following limits. (If an answer does not exist, enter DNE.)
(i)
x→0+
lim
sgn x
(ii)
lim
sgn x
(iii) lim sgn x
(iv) lim |sgn x|
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(b) Find each of the following limits. (If an answer does not exist, enter DNE.) (i) x→0+ lim sgn x (ii) lim sgn x (iii) lim sgn x (iv) lim |sgn x|

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Expert Answer

Step 1

Consider the given function.

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(-1 if x<0 sgn.x ={ 0 if x= 0 1 if x>0

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Step 2

Part (a):

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lim(sgn.x) Atx >0, sgnx = 1 .. lim (sgn x) =1 x-0*

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Step 3

Part (b):

...
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lim(sgn.x) At x < 0, sgn x =-1 .: lim (sgn x) =-1

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Tagged in

Math

Calculus

Limits

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