course hero pdf - Google Doc x = Untitled document - Google [ X Dashboard X Untitled document - Google [ X MATH140-12141 (ONL) Busin x BusCalc.pdf X K CO docs.google.com/document/d/1XVYliR2nkPFruDoNqTFalYp8ihMOwUfCnebNvAyD4uo/edit Update : Suggested Sites M Gmail YouTube Disney+ canvas Other Bookmarks Example 4 Evaluate using continuity, if possible: Chapter 2 The Derivative Business Calculus a) lim x' - 4x b) lim * -4 b) lim 4 x/2 x+3 a) The given function is polynomial, and is defined for all values of x, so we can find the limit 5. Evaluate (a) lim x2 + 3x + 3 mx + 3x + 3 (b) lim- by direct substitution: x -2 r -2 lim x3 - 4x = 23 - 4(2) = 0 x +7 x+7 6. Evaluate (a) lim x2 + 9x + 14 (b) lim 2 + 9x + 14 b) The given function is rational. It is not defined at x = -3, but we are taking the limit as x approaches 2, and the function is defined at that point, so we can use direct substitution: x +7 x+7 lim *-4 _2-4 2 (c) lim -2 1 74 x2 + 9x +14 17 x2 +9x +14 x 12x+3 2+3 c) This function is not defined at x = 2, and so is not continuous at x = 2. We cannot use direct substitution. 7. At which points is the function shown discontinuous? 2.2 Exercises 1. Use the graph to determine the following limits. (a) lim f(x) (b) lim f(x) 8. At which points is the function shown discontinuous? (c) lim f(x) (d) lim f(x) 9. Find at least one point at which each function is not continuous and state which of the 3 2. Use the graph to determine the following limits. conditions in the definition of continuity is violated at that point. (a) lim f(x) (b) lim f(x) (a) x + 5 x - 3 (b) X -2 (c) (c) lim f(x) (d) lim f(x) (d) 2_6x +9 (e) In( x2 ) 5. Match the situation descriptions with the corresponding time-velocity graph. (a) A car quickly leaving from a stop sign. 9. Use the graphs to estimate the values of g(x), (b) A car sedately leaving from a stop sign. g '(x), (fog)(x), f'( g(x) ), and ( fog ) '( x ) at y=f(x) y g(x) (c) A student bouncing on a trampoline. (d) A ball thrown straight up. x = 1. (e) A student confidently striding across campus KAF 10. Use the graphs to estimate the values of g(x), to take a calculus test (f) An unprepared student walking across g '(x), (fog)(x), f'(g(x) ), and ( fog ) '( x ) for campus X =2.course hero pdf - Google Doc x _ Untitled document - Google [ X Dashboard X Untitled document - Google [ X MATH140-12141 (ONL) Busin X BusCalc.pdf X -CD docs.google.com/document/d/1XVYliR2nkPFruDoNqTFqlYp8ihMOwUfCnebNvAyD4uo/edit Update : Suggested Sites M Gmail YouTube Disney+ canvas Other Bookmarks 5. Match the situation descriptions with the corresponding time-velocity graph. (a) A car quickly leaving from a stop sign. 9. Use the graphs to estimate the values of g(x), (b) A car sedately leaving from a stop sign g '(x), (fog)(x), f'(g(x) ), and ( fog ) '(x ) at (c) A student bouncing on a trampoline. (d) A ball thrown straight up.