Recall the various versions of the definition of derivative from Topics 2.1-2.3: f'(x) = lim (*+4x)-fx "(c)= 1im /(c+h)- f(c)and Ax f'(c) = lim (x)-f(c) h x-+c x-C 12.) Find the following using the Limit Definition of Derivative. You should be able to do this with very little computation. ? I'm confused what its asking a.) lim sin (x+ Ax) - sin (x) Ar - b.) lim- ( xth ) -x2 Ax h -+ 0 h f ( * ) = lim cos ( x+ 8x ) - cos x x th - x2 h Ox f' ( x ) = 1m h = lim hav = Im cosex + cosax - cost Ox-JO SX = lim h hoo Los Ox Ox cos sin x - sin sin I + h c.) lim 4 cos x - cosy 6 d.) lim cost + cosh - 2 x - X - 1 h -+ 0 h = lim A (2 +Ax)' -8 2 + 0x3 - 8 f.) lim- cos x + e.) lim- = lim = lim -Sin x + 1 Ar-+0 Ax I X X-1 Ax -DO X 5 7 * - 7 7 what is 8+3 x -8 it asking DX 1x =x 3x2 '1 3x2 In x -In 2 g.) lim X - 2 X -+ 2 (3+4x)"+(3+4x)-12 x-2 = lim x - 2 h.) lim Ar-+0 = lim 3"+ 4x + 3+4x - 12 Ax 7 what is it = lim 9 + 0x2+ 3 +0-12 asking Ax = lim AX + OX OX CS Ox Scanned with CamScanner X30 DX