Limits? ?The following limits represent the derivative of a function f at a point a. Find a possible f and a, and then evaluate the limit. tan (? 3x?11) lim x?5 x?5

Solution Step 1: tan ( 3x11) Given lim x5 x5 The given limits represent the derivative of a function f at a point a. From the data the function f(x) is tan ( 3x 11) and the point a=5 tan ( 3x11) We have f’(5)=lim x5 x5 f(x)f(x ) By the definition of limit f’(x)= lim 0 xx0 x0 Step 2: Therefore to evaluate the limit we need to find f’(5) Here f (x) =tan ( 3x 11) 2 d f’(x)=sec ( 3x 11) dx( 3x 11) 2 1 d =sec ( 3x 11) 2 3x11 dx (3x 11) =sec 2 ( 3x 11) 1 (3) 2 3x11 f’(x) = sec 2 ( 3x 11) 3 2 3x11