Which value must you assign to a so that f(x) is continuous at x = 5? 5+4x-x x-5 f(x) = If a = a x #5 x=5 then f(x) is continuous at x = 5. Find the limit. 2x-1 lim x0 ex-1 - 1 lim X X-0 e - 1 Evaluate the limit. 2x2 +2 lim X0 8x+4-9x 2 Determine the limit. 3 7x-5x 13x + 5x lim X- --00 lim f(x) = (Type an integer or a simplified fraction.) X-00 Evaluate the limit. e -X lim X0 5+6eX Evaluate the limit. 8 lim X- 8+eX A population model is used to describe how the rate of reproduction of organisms depends on the amount of nutrients that are available. The model shows how the rate of division of E. coli cells depends upon the amount of sugar added to their growth flask. If r is the rate of reproduction (number of divisions in one hour) and C is the amount of glucose sugar added to the growth medium measured in moles, then the following applies. r(C)= 1.31C C+0.27x10-4 (a) Show that the reproduction rate goes to zero when the sugar level is low; that is lim r(C) = 0. C-0 Since r is continuous at C=0, lim_ r(C)=r() = C+0 1.31 ( +0.27x10-4 = 0.