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Exam 1 Conceptual Review

Quiz by Nicholas De Santos

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12 questions
Show answers
  • Q1
    Which one of the following is NOT a way to evaluate a limit as x approaches "a" of a function?
    numerically
    graphically
    finding f(a)
    algebraically
    120s
  • Q2
    What tools do you use to solve a limit numerically?
    the graph of the function
    factoring the function
    direct substitution
    table of values
    120s
  • Q3
    True or False: A point (a, f(a) ) of a function needs to exist on the graph in order for the limit as x -> a to exist.
    False
    It depends
    True
    120s
  • Q4
    Which of the following needs to exist in order for the regular limit as x-> a to exist?
    the right hand and left hand limits need to exist
    the left hand limit needs to exist
    the right hand limit, left hand limit, and f(a) needs to exist
    the right hand limit needs to exist
    120s
  • Q5
    What needs to hold true in order for a function to be continous?
    the limit of x-> a needs to exist
    the limit as x-> a = f(a)
    f(a) needs to exist
    All of these need to hold true
    120s
  • Q6
    True or False: All continuous functions are differenciable on their domain
    True
    False
    It depends
    120s
  • Q7
    When examining the average rate of change formula and the difference quotient formula, which of the following statements is true?
    f(x+h)-f(x) = (x2-x1)
    (x2-x1) = h
    (y2-y1) = h
    f(x+h) = y1
    120s
  • Q8
    Complete the definition of a Derivative: The derivative is the limit as _________ approaches 0 of the ____________
    h, function
    h, difference quotient
    x, difference quotient
    x, function
    120s
  • Q9
    The derivative of a given function at a certain point gives you what?
    the slope of the tangent line
    the y intercept of the tangent line
    the slope of the function
    the y intercept of the function
    120s
  • Q10
    which of the following will result in a non-differentiable function
    the function has a corner/cusp at a certain point
    All of these will result in a non-differentiable function
    the function is discontinuous at a certain point
    the function will result in a vertical tangent line at a certain point
    120s
  • Q11
    When considering a position function s(t), which of the following is true?
    s''(t) = v'(t) = a(t)
    v''(t) = s'(t) = a(t)
    v''(t) = a'(t) = s(t)
    s''(t) = a'(t) = v(t)
    120s
  • Q12
    What does the derivative of a function NOT represent?
    the instantaneous rate of change
    Where the function is continous
    The slope of the tangent line
    relationships in position functions
    120s

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