Always, Sometimes , or Never True

Solve for x Always, Sometimes, or Never True Limits Derivatives 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 50 50 50 50 Click here for game DIRECTIONS Hardtke Jeopardy Template 2011

10 Always, Sometimes, or Never Click to check answer SOMETIMES Hint: Not true if Click to return to game board

20 Always, Sometimes, or Never A rational function f has an infinite discontinuity.Click to check answer SOMETIMES Hint: it might have only a removable discontinuity. Click to return to game board

30 Always, Sometimes, or Never For f(x) = e x as x ∞ , f(x)  0.Click to check answer NEVER Hint: As x  ∞, f(x)  ∞ As x  - ∞, f(x)  0 Click to return to game board

40 Always, Sometimes, or Never Click to check answer SOMETIMES Hint: true when f is continuous at a. Click to return to game board

50 Always, Sometimes, or Never If f(0) = -3 and f(5) = 2, then f(c) = 0 for at least one value of c in (-3, 2).Click to check answer SOMETIMES Hint: IVT will prove this true only if is continuous over that interval. Click to return to game board

10Solve for n f(x) = has an infinite discontinuity at n.Click to check answer 2 Hint: f(x) = has a removable discontinuity at -2 and an infinite discontinuity at 2. Click to return to game board

20Solve for n f is continuous for this value of n.Click to check answer 3 Hint: 4n + n = 12 + n when n = 3 Click to return to game board

30 Solve for n For f(x) = as x  – ∞ , f(x) nClick to check answer – 5 As x  – ∞ , f(x) ≈  – 5 Click to return to game board

40 Solve for n = nClick to check answer 16 = 16 Click to return to game board

50 Solve for n Given polynomial function f, wheref(8) = -2 and f(-2) = 3, then there exists at least one value of c (-2, n)such that f(c) = 0.Click to check answer Hint: By IVT there must be an x-coordinate between -2 and 8 that produces a y-coordinate between -2 and3. Click to return to game board

10 Limits Given Find .Click to check answer d.n.e. As x 0 -, f(x) ∞. As x 0 +, f(x) - ∞ Click to return to game board

20 Limits Given Click to check answer -1 Click to return to game board

30 Limits Click to check answer Click to return to game board

10 Derivatives Click to check answer nxn-1 Hint: This is the Power Rule Click to return to game board

20 Derivatives > 0 only on intervals where f(x) is ____.Click to check answer Hint: rising or going up or has a positive slope are acceptable but not as nice Click to return to game board

30 Derivatives Click to check answer 12 Hint: for f(x) = x3, you must recognize this as f ‘ (2) where f ‘(x) = 3x2 and thusf ‘(2x) = 3(4) = 12 Click to return to game board

40 Derivatives Click to check answer Hint: divide first then use Power Rule on each term  4) Click to return to game board

50 Derivatives Click to check answer Hint: Subtract exponents first. Click to return to game board

Jeopardy Directions • Any group member may select the first question and students rotate choosing the next question in clockwise order regardless of points scored. • As a question is exposed, EACH student in the group MUST write his solution on paper. (No verbal responses accepted.) • The first student to finish sets down his pencil and announces “15 seconds” for all others to finish working. • After the 15 seconds has elapsed, click to check the answer. • IF the first student to finish has the correct answer, he alone earns the point value of the question (and no other students earn points). • IF that student has the wrong answer, he subtracts the point value from his score and EACH of the other students with the correct answer earns/steals the point value of the question. (Those students do NOT lose points if incorrect, only the first student to “ring in” can lose points in this version of the game.) • Each student should keep a running total of his own score. • Good sportsmanship and friendly assistance in explaining solutions is expected! Reviewing your math concepts is more important than winning. Return to main game board

Always, Sometimes , or Never True