Calculus help

Question

For the following piecewise defined function, evaluate the specified one-sided limts:

 

 

f(x)=x²+2x, x≤1

      

        x+3, x>1

Find lim

      x→1^-

 

       lim

      x→1⁺

 

       lim

      x→1

 

Answer 1

For limit  x→1^- , evaluate the parabola part.

For limit  x→1⁺ , evaluate the linear part.

For limit  x→1 , both left and right limits must be the same.  If not same, then undefined.

Answer 2

lim_x→1^- f(x) = lim_x→1^- (x²+2x) = 3

 

lim_x→1⁺ f(x) = lim_x→1⁺ (x+3) = 4

 

lim_x→1 f(x) does not exist since the one-sided  limits are unequal