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Calc- Test Review

  1. Use the IVT to show that the functions f(x)= Image Upload 1 has a zero on the interval [-2,-1]
    1) f(x) is cont. because poly functions are cont.

    2) f(-2) = 2      f(-1) = -4

    Since f(x) is cont. and f(-2) ⟨ f(c) ⟨ f(-1), then ∃ some C∃ (-1,-2) s.t f(c) = 0
  2. Image Upload 2

    Discontinuity at x= (first)
    x= 8

    Removable (bc x-8 cancels)
  3. Image Upload 3

    Discontinuity at x= (second)
    • x= -1
    • Non-Removable (stays in denominator)
  4. Sketch the graph of any function

    lim     f(x) = 4    and    lim   f(x) = -1
    x→ 2+                        x→ 2-


    Is the function cont.?
    • Image Upload 5
    • No, the limit DNE

    • (x--> c = x-axis
    • f(x)=b = y axis)
  5. sinx/x = y1
    sin3x/x = y2

    (Must be going to 0)
    • y1 = 1
    • y2 = 3
  6. 1-cosx = y

    (Must be going to 0)
    y = 0
  7. 7 + 2x - 5x²
    --------------
    2x² + 3x - 4

    x--> - ∞
    -5/2

    When top and bottom are both x² heavy you take the coefficient and divide.
  8. Image Upload 6
    = Image Upload 7

    = 0 -3

    = -3


    (Anything to the -∞ is 0 except 1 and 0)
  9. Image Upload 8
    = Image Upload 9

    = -∞ +2

    = -∞

    (e^∞ is ∞, e^-∞ is -∞)
Author
GoBroncos
ID
356577
Card Set
Calc- Test Review
Description
Updated

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