Question

1 6. Where is the function f(x) { { - X4 if x # 0 discontinuous? if x = 0 0 Is this a removable discontinuity? ex if x < 0 7. Where is the function f(x) discontinuous? x2 if x > 0 Is this a removable discontinuity? Is it a jump discontinuity? f(x) = {

Answer 1

Solution: if xfo 004 fo= if x=0 find Left limit at x=0 lim fran - lim 11 x4 - (orga at at 0 + Right limit at oc=0 lim dot fo 11 lim - of x4 = (0+4 ot 19 lim f(x) = Does not exist and lim free fro)=0 do It is not continuous at x=0.It is infinite type discontinuity. It is not seemovable dis continuity. CHon - Seemovable dis continuity)

en (9) if xxo f(x) = 2² il zo find left limit at xao lim fox f(x) = ex if aco) -o- lim 0 % or f(x) = x², if azo) Right limit at x=0 lim f(a) x-xot lim x- sot (0+32 frac) = x2, if so frou (0² lim f(x)=17 lim f(x) =o=fo) Xot Xon So it is finite Jump dis continuity Monjamo vabile discontinuity, and finite gumb dis continuity