For the following two (02) items: Let f(x) = cases 1 - 2x x^2 , & x 0 cases What is _ x 0^+ f(x) equal to?

Step-by-step solution

For x > 0 , the function is given by f(x) = x 16 + x - 4 To find the right-hand limit, we evaluate _ x 0^+ f(x) _ x 0^+ x 16 + x - 4 Rationalizing the denominator by multiplying the numerator and the denominator by 16 + x + 4 : _ x 0^+ x ( 16 + x + 4) ( 16 + x - 4)( 16 + x + 4) _ x 0^+ x ( 16 + x + 4) 16 + x - 16 _ x 0^+ x ( 16 + x + 4) x Canceling x from the numerator and the denominator: _ x 0^+ ( 16 + x + 4) Substituting x = 0 : 16 + 0 + 4 = 4 + 4 = 8 Answer: 8