Question 1158629
Suppose {{{f(x)}}} is defined as shown below

{{{f(x) =e^x}}} if {{{x >=0}}}
........{{{x + 1}}} if {{{x < 0}}}


Determine whether or not that {{{f}}} is continuous at {{{0}}}.


for the values of {{{x >=0}}}, we have to select the function {{{f(x)  = e^x}}}


right-hand limit:  ({{{x}}} comes from the right, {{{x > a}}})

  {{{lim(x->0, f(x) )= lim (x->0,e^x )=1}}}.......a)


for the values of{{{ x< 0}}}, we have to select the function{{{ f(x)  =x + 1}}}

left-hand limit: ({{{x}}} comes from the left, {{{x < a}}})


 {{{lim (x->0,x+1)=1}}}..........b)


{{{lim (x->0,e^x )= lim (x->0,x+1)}}}


Hence the function is {{{continuous}}} at {{{x = 0}}}.