10 9 8 7 6 5 4 3 2 10-9 -8 -7 -6 -5 -4 -3 -2 -1, 1 2 3 4 5 6 7 8 9 10 -2 3 -4 -5 -6 -7 -8 -9 -10+ For the graph f(x) above, find: Find: lim f(x)=-3 x-3- lim f(x)=3 x+3+ lim f(x)=DNE +3 lim f(x)=-9 x-6 lim f(x)=-9 +91-2 =-9 lim f(x)= x-6 f(3) = -3 f(6) 6 = بھی 0° x x 0
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- f(2 + h) – f(2) 2 if f(x) = x² +7. Find lim h h→0 f(2 + h) – f(2) lim (Simplify your answer.) h→0Vr- 2x -4 Let f(x) = Find lim f(x)? *+1The graph of y = f(x) has the following features: • lim f(x) = 2- #48 ● ● lim f(x) = 5 8174 ● lim f(x) = ∞ 24-3 lim f(x) = -00 2-3+ Which of the following might be a graph of y = f(x)? 6 5- 4 3 2 H -8-7-6-5-4-3 -2 -1 -1 -2 -3 -4 -5 -6 -7 8+ 8+ 7 6- 5 4 3 2 + -8 -7 -6 -5 -4 -3 -2 -1 4 -2 3 -4 -5- -6- -7- -84 1 2 3 4 5 6 7 8 12 a 4 5 6 7 8
- (x3 - 3x2 +6- 2x) 10. Use a table to estimate lim X-+3 X- 33-3x-2 lim,--1 x+12. A portion of the graph of the function y = f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x-2+ x-2- x-2 (ii) lim f(x); lim f(x); x-3 lim f(x). x+3 3. The graph of the function y = k(x) is shown in the figure. (a) Write a piecewise formula for the function k. (b) Evaluate the one-sided limits of k at x = 1 algebraically, by using your formula from part (a). y=f(x) 1+ fif 1 -1- 2 1.5 1 4. Let f(x) = |x| and g(x) = x - 3. (a) Determine the formulas for each of the related composite functions: h(x) = (fog)(x) = f(g(x)) s(x) = (gof)(x) = g(f(x)) t(x) = (gofᵒg)(x) = g(f(g(x))). 5. (a) Find the values of x₁ and x₂ in the figure. (b) Find the largest positive number 8 such that: |-1|<0.1 whenever 0<|x-1|<8. Hint: Choose to be the minimum value of |x-1| for i = 1,2. (b) Plot graphs of all the functions: f,h, s, and t in the same coordinate plane. Use…