Math Quiz: Take The Limits And Continuity Assessment Test

10 Questions | Total Attempts: 108

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Math Quiz: Take The Limits And Continuity Assessment Test

A limit is a number that a function approaches as the autonomous variable of the function approaches a given value. Take this assessment test to evaluate your insight.


Questions and Answers
  • 1. 
    Evaluate the limit ( x – 4 ) / (x2 – x – 12) as x approaches 4.  
    • A. 

      0

    • B. 

      Infinity

    • C. 

      1/7

    • D. 

      Undefined

  • 2. 
    Differentiate the equation y = x2 / (x +1).
    • A. 

      2x

    • B. 

      (x2 + 2x) / (x + 1)2

    • C. 

      x / (x + 1)

    • D. 

       (2×2) / (x + 1)

  • 3. 
    Evaluate the limit (1n x ) / x as x approaches positive infinity.
    • A. 

      1

    • B. 

      0

    • C. 

      E

    • D. 

      Infinity

  • 4. 
    Differentiate (x2 + 2)1/2.
    • A. 

      (x2 + 2)1/2) / 2

    • B. 

      x / (x2 + 2)1/2

    • C. 

      (2x) / (x2 + 2)1/2

    • D. 

      (x2 + 2)3/2

  • 5. 
    Locate the points of inflection of the curve y = f(x) = x2 ex.
    • A. 

      -2 ± √2

    • B. 

      2 ± √2

    • C. 

      2 ± √3

    • D. 

      2 ± √3

  • 6. 
    Differentiate y = sec (x2 + 2).
    • A. 

      2x cos (x2 + 2)

    • B. 

      –cos (x2 + 2) cot (x2 + 2)

    • C. 

      2x sec (x2 + 2) tan (x2 + 2)

    • D. 

      Cos (x2 +2)

  • 7. 
    If y=xsinx, find dx/dy.
    • A. 

      Sinx - cosx

    • B. 

      Cosx - xsinx

    • C. 

      Cosx + xsinx

    • D. 

      Sinx + xcox

  • 8. 
    A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)? 
    • A. 

      y=3/2x2 + 2x

    • B. 

      Y=3/2x2 + x

    • C. 

      Y=3x2 + x/2

    • D. 

      y=3x2 + 2x

  • 9. 
    Find dy/dx if y = 52x-1.
    • A. 

      52x-1 ln 5

    • B. 

      52x-1 ln 25

    • C. 

      52x-1 ln 10

    • D. 

      52x-1 ln 2

  • 10. 
    Find the point in the parabola y2 = 4x at which the rate of change of the ordinate and abscissa are equal.
    • A. 

      (4,4)

    • B. 

       (2, 1)

    • C. 

      (1,2)

    • D. 

      (-1, 4)