Question

Determine

ModifyingBelow lim With x right arrow c Superscript pluslimx→c+​f(x),

ModifyingBelow lim With x right arrow c Superscript minuslimx→c−​f(x),

and

ModifyingBelow lim With x right arrow climx→c​f(x),

if it exists.

cequals=22​, ​ f(x)equals=

left brace Start 2 By 2 Matrix 1st Row 1st Column 3 minus x 2nd Column x less than 2 2nd Row 1st Column StartFraction x Over 2 EndFraction plus 1 2nd Column x greater than 2 EndMatrix 3−x x<2 x2+1 x>2

Answer 1

f (x 0 = { 3 - x, x < 2 x + 1, x > 2 Lt x rightarrow 2^+ f (x) = Lt x rightarrow 2^+ (x + 1) = 2 + 1 = 3 Lt x rightarrow 2^- f (x) = lt x rightarrow 2^- (3 - x) = 3 - 2 = 1 potion C Lt x rightarrow 2^+ f (x) = 3 lt x rightarrow 2^- f (x) = 1