Page 1 :
e lut 4: A - IR be a tunian. ow tin said to, be differentiable at x=a it im Hlm)- Ha) exists, finitely. The linit it exints, in eallid the" Leui valive d, ļ at the pt a., D, # 91 a funhon ti A - IR in differentiable at, 1= a E A then f must be coninuous at n= a, but not th converse., ti A- IR n difterentialle at, diff., fi A-IR ù Routinuous at n=a, uin f(m)-f(a) exists tinitely., To move,, lin f(^)= f(a)., [, f(w) - +(@) . (x-a) + f(^)|, lin f(m), hin, sow, 1-a L (X-a), f'(a). uim (n-a) + f(a), f (a). o + (a), f(a), : { n cantimowa at x= a., But the canverse in not true., f: IR - IR detined by (x)= Ix! n continyans, but not derivable at X=0.(Try to move)., at 1=0, -1; 17U ů not deivable, (1-x ; X<I, Show that, f(x)=, at X = I, him f(a)-f(1), lim (^?1)- (1-1), 2