Online Practice Test 1a for MATH 171.

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Test Questions:

1. Which one of the following intervals contains a solution to:
        x3 + x2 + 7

    (-2, -1)
    (-3, -2)
    (-3, -4)
    (0, 1)
    (1, 2)

2. Evaluate the limit as x -> infinity of (5x3 - 2) / (4x3 - 3x2 - 1)

    5/4
    4/5
    1
    2
    -5/4

3. An equation of the line through the points (2, 5) and (-8, 6) is:

    y = 0.1x + 5.2
    y = 4.3x + 5.2
    y = 5.2x - 0.1
    y = -0.1x + 4.3
    y = -0.1x + 5.2

4. Find a positive value of x which will make the following vectors orthogonal:
        < x, 1 > and < x + 1, -6 >

    -3
    -2
    1
    2
    3

5. Evaluate the limit as x -> 2 of (5x3 - 2) / (4x3 - 3x2 - 1)

    5/4
    4/5
    1
    2
    -5/4

6. A line is given by the parametric equations: x = 1 - t, y = 2 + 3t
    Find the slope of the line.

    -3
    -2
    1
    2
    3

7. Find the limit as x->0 of x * cos(1/x) - the Squeeze Theorem may be useful.

    negative infinity
    -1
    0
    1
    positive infinity

8. Find the equation of the line that is tangent to x3 - 3x2 + 11 at x = 4.

    y - 4 = 24 * (x - 27)
    y - 27 = 24 * (x - 4)
    y - 24 = 27 * (x - 4)
    y + 27 = 24 * (x + 4)
    y + 24 = 27 * (x + 4)

9. Which of the following statements is true concerning the function:
       

    f(x) is continuous at 3
    f(3) = 10
    lim x --> 3 - f(x) = 8
    lim x --> 3 + f(x) = 8
    f(x) is undefined at x = 3

10. Find f'(a) for: x / (2x - 1)

    1 / (2a - 1)2
    -1 / (2a - 1)2
    1 / 2
    1 / 2a
    -1 / 2a

11. Assume h(x) = f(x)*g(x) and f(2)=2, g(2)=3, f'(2)=5, and g'(2)=7. What is h'(2) ?

    41
    34
    31
    29
    23

12. A ball is launched into the air with a velocity of 10i + 40j ft/sec. Its position after t seconds is given by:
        r(t) = (10 * t)i + (40 * t - 16 * t2)j
How many seconds (to the nearest tenth) will have passed when the ball has a vertical velocity of zero?
You may assume the j component is the vertical component and the ball never hits the ground.

    0.8 seconds
    1.3 seconds
    1.7 seconds
    2.5 seconds
    10.0 seconds