MATH 231 Quiz: CALC I -- Limits
Document Summary
Find a real number c that makes exist and equal to a nite number. C 5x x2 x + 6. To get rid of the roots in the numerator, we multiply by the conjugate of x + 7 is x + 7 + 7. = lim x 0 x + 7 7 x(cid:0) x + 7 + 7(cid:1) The numerator is simply x + 7 7 = x, and this x cancels with the one in the denominator. This allows us to then plug in x = 0, which gives. If we pick c = 6, then the numerator is 6 5x x2, which factors as (x + 6)(x 1). = lim x 6 (x 1) = 7, so c = 6 is our choice. A piecewise function given by if x 1 x2. 3 x if 1 < x < 2. 4 if x = 2 ln(x) if x > 2 f (x) = is plotted below.
