Show that
`Lt_(xto0+)(|x|)/x=1`

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Show that Lt_(xto0)(sinax)/x=a(ainR) .

Show that lim_(xto0) (e^(1//x)-1)/(e^(1//x)+1) does not exist.

Given f(x)={((x+|x|)/x,x!=0),(-2,x=0):} show that lim_(xto0)f(x) does not exist.

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) f(x) does not exist.

Statement 1: lim_(xto0)[(sinx)/x]=0 Statement 2: lim_(xto0)[(sinx)/x]=1

Letf(x)={{:(x+1,", "if xge0),(x-1,", "if xlt0):}".Then prove that" lim_(xto0) f(x) does not exist.

The value of ordered pair (a,b) such that lim _(xto0) (x (1+ a cos x ) -b sin x )/( x ^(3))=1, is:

Evaluate Lt_(xto0)(sin(x^(0)))/x

Prove that [lim_(xto0) (tan^(-1)x)/(x)]=0, where [.] represents the greatest integer function.