Question

Find the results of next functions

2.-Find the values of a and b such that fis differentiable at x 1 ax+b si 1s. Sol, a- 2, b-1. f(x)=1si x<1 x-7 si 0<x Sb| f(x) =16/x si x< 3 If ... a) decide a value of b far which f is continuous b)fis differentiable in the value of b that ycu find in part a)? 4.- In the following functions determine what is requested sen(x) si x < mx+b si x 2 a s the function continuous in xen? sol: yes, with m 1 = "? Sol: yes, with a Is the function differentiable in x and b 2 b) 4 ax +b si 4 (x) = cos(r) sE x 4 5.- 2-4b ? sol: yes, with a 4 a) is the function continuous in x _ 1 -Sol: yesa b) is differentiable the function in x - 4

Answer 1

fln) 2 11 J is ditfereatiable at We know that if a thin it i wntinuow Cit a differntiable at nl Lontinuons at ombinuity at n f(D a.1 b a+h Lim fln) dim Z-Y im (1-A)2 0KY Limf(1A) MO +1<& Lim a(it A) +b atb continuons at 1 = | fis Lim fin) Lim fin) tK-K at b at Diferatiahility f(n)-fli) im L.HD a1 n-1

f C1-A)-fi) A-1- dim L.H.D (42-(a.146) Lim OKT 1-34+42 - h. Lim usig X-2hth2 Lim Lim Aln)- fl) lim M-IT R.H.D lim ch>O (QJ(THI a.146) Lim a(1+) - Lim a+ah + -&- ak fis at r L.H D R.HD a

Fom at b b1-2 -) a