Show that : `Lt_(x->0^+){(2|x|)/x +x+1}=3`

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

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

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

Show that : x- x^3/6 lt sinx for 0 lt x lt pi/2

Show that the function f(x)={:{(1-x", " x lt1),(x^2-1 ", " x ge 1):} is continuous but not differnetiable at x=1

Show that the function f(x)={:{(3+x", " xge0),(3-x", " x lt 0):} is not differentiable at x=0

For 0 < x lt=pi/2, show that x-(x^3)/6< sin(x) < x dot

Show that f(x)={1+x^2,if0lt=xlt=1 and 2-x if x >1 is discontinuous at x=1

If y=e^(asin^(-1)x)\ ,\ -1\ lt=x\ lt=1, then show that (1-x^2)\ (d^2\ y)/(dx^2)-\ x(dy)/(dx)-\ a^2y=0

Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):} is continuous at x = 2