Question

1. Find any absolute maximums or minimums of f(x)=xV1 - X on (-1,1). Use calculus methods illustrated in your book and notes and show all work. Do not use a graph to justify your answer. 2. Evaluate the limits using calculus methods illustrated in your book and notes and show all work. Do not use a graph to justify your answer. a. liman 2-0*+sin(2x) tan(4x)

Answer 1

Solution 1- Given tine adin. on [-1,1] t is continuous on (-1,1]. Now tind d'ini= sin + n. 7. 11-272. (-1). f(n = 5-a. - 7 for critical points. H(M)=0 & 1-1 - 27. 1 1/2 = 0 7 2.11-21) – co 251-X a 2-291-X = 0 a 2-3x to a 3x=2 a x= Now , f(-1)= (1 x 51-61) = -52. f(1) = 0. +( 2 ) = 2/3 51-23 = 2 x 5 / 3 = 2 2 2 2 2 rooom this list of values o we seed that the absolute maxima, is 2 and will ocar at t=2 tan (40) X+ sin(an) ato. a z lim 23 - 2. (Bay) le tesim), bar con le forum) Apply L Hospital rule, tan (44) o ursin (21)

Sec744 x 4 110 Lt Cos(2x) 42 4 sec (0) L = lim 170 17 20.12%), 4 sec²(o) a L- 1 + 2 colo 4 x 1 a La +2x 1 tan (40) - x40 nt Sin (2x) tlon a lim À