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

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.

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

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:

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

In the neighbourhood of x=0 it is known that 1+|x|lt(e^(x)-1)/(x)lt1-|x|"then find"lim_(xto0)(e^(x)-1)/(x).