Question

x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car is traveling so that its position is given by s(t) = 3:4 - 321? +90r2 for OSIS5. (a) Find when the car's velocity is zero. (b) Find when the car's acceleration is zero. (c) Plot s(t), s'(1) and s(1) together on the window [0,5][-100,200].

Answer 1

② Ciren x²+2x+2 y=f(x) = x²-3x-5 32+ 2(3)+2 9+6+2 9-3 (3) - 5 9-9-5 f(3) = - 17 -5 17 5 (6) fros- f(3) x²+2x+2)+ 17 N-3 x²-3x-5 (4-3) ① lim a x²+2x+2 x²-32-5 -) + 1/ / + #73 17 5 [indeterminate a-3 3-3 foom na olo 03 81& g(x) ata Clinton um d da . + da x73 da -) d dx 10 By 2-Hospital Rule If rim flas then him fx) f'(x) g(x) nta gle) 22 +2x+2 3- 3х- (x-3) limos x²+2x+2 a la E che test) = f'xsgan) – geussen x-3 x2-3x-5 g(x)? tim ad me (x2+2x+2) (42–34-5) - (x83x~5) (x²+2x+2) (x2_32-592 lim (2x+2) (x2-32-3) - (9_2-3)(x+24+2) 13 (22-32-592 (6 +27 (9-9-5) -(6-3) (9+672) 8(-5)-(3)(17 (9-9-992 -40-51 25 dx → a-3 个 91 25

[DOHC3th) - (3) b c (3+3}+2/3+1)+2 (8+48-3(+4)-5 + 13+534203449 42 lim h30 17 十 学生, 3159_303+4)-5 3 M L-Hospital Rule lim h90 品(ハンナ( 13+79+2(3+1)+2 B+692-313+h)-5 り+し号) 2 lim h0 赤(い 多(がら B+b8-9-36-5 会(Oth+2H+ &りし- ah -14 ) - L.CO+h-ah-14) Cathtah te) (18+55-9-3h-592 h30 Etirol ( 2 (3th) +2 2 3 + b) - sh-14) - C2 (3th) - 3日)) (@tbs-t2ht &) h-90 ((3+5*-9-34-592 3 ( 2 3t22 C (3) - 0-14) - (23)- 12 (9+ ot&) (9-9-592 (3) (14) 8 C-5) - 91 -40-51 25 25