1. Consider the function /(x) defined by the following graph: 12 -2 -I 2 Find: a) lim /(x) b) lim f(x) 1-+-1 c) lim /(x) d) lim /(x) 2. Evaluate the following limits. a) lim (x -2r* + 3x-1) bj lim I-4-I' c) lim vsin.x d) lim 208x 3. Consider the function: Amer y-Isxsi Find the following limits, if they exit. a) lim /() b) lim f(1) c) lim /(0) I-HD 4. Evaluate. - 4 x+x-2 a) lim b) lim- 341 x42 x-1 - 8 c) lim- d) lim - x- -2x-3 2 - 4 3x -4x+3 1 1 e) lim X + 27 f) lim 2 143 x+3 14l x-2 5. Evaluate. a) lim- X-4 b) lim- INx - 2 V3+1 -V3 c) lim dj lim 1-40 e) lim f) lim I X-1 6. Evaluate. X-8 3/2 a) lim b) lim TH X-4 C) lim- Vx -17. Consider the function y (x) defined by the following graph: 4 -4 -3 -2 -1 10 13 For each value of x= a , classify the function /(x) as continuous, having a jump, a removable or an infinite discontinuity. a) a=-3 bja=-1 c) a =2 d) a=0 e) a=3 8. For what value of the constant c is the function er +1 1 x22 continuous at every number? 9. For each function, calculate first the slope of the tangent line with the formula: m = lim (x)- f(a) then find the equation of the tangent line at the given point. a) /( x) = x+x. at P(-1,0) b) /(x) = = X-1 at P(1,0) x+1 10. For each case find the slope of the tangent line at the general point P(a, /(a)) using m = lim (a+ h)- /(a) a) /(x)=x b) / (x)=x c) /(x)=x -2x+1 d) / (x)= = 11. For each case, find the ARC over the given interval. a) /( x=x-x+x. [-1,1] b) S(x) = = 2x -1 2r + 1 [0,2] 12. For each case, find the IRC at the given number. a) /(x)=x-x. at x = 1 b) /(x) = X at x =0 +1 13. For each case, find the average velocity over the given interval. a) s( n)=1+1, [0,2] b) str=-1. [1,2] 14. For each case, find the instantaneous velocity at the given moment of time. a) s(1) = 27 -1, at 1 =1 b) s(1) = 20* -30. at 1 = 0