Online Practice Test 2a for MATH 151.

This online test was created by Brent M. Dingle.
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Test Questions:

1. The derivative of x2 * sin(x) is?

    cos(x)
    2x * cos(x)
    x2 * sin(x) + 2x * cos(x)
    x2 * cos(x) + 2x * sin(x)
    -2x * cos(x)

2. Calculate limx --> 0 x * cot(x)

    negative infinity
    -1
    0
    1
    positive infinity

3. Differentiate y = (x4 + 1)100

    100 * (x4 + 1)99
    100 * x3 * (x4 + 1)99
    400 * (x4 + 1)99
    100 * (4x3)99
    400 * x3 * (x4 + 1)99

4. Find the equation of the tangent to the circle: x2 + y2 = 25 at the point (3, 4).

    y = 3/4
    y = -3/4
    3x + 4y = 25
    4x + 3y = 25
    4x - 3y = 25

5. Given that a particle's position at time t is defined by:
        r(t) = (2t3 - 12t)i + (t2 + t)j
    What is the speed of the particle at t = 2?

    -6i + 6j
    7i + 3j
    sqrt(137)
    11
    13

6. A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 foot per second, then how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 8 feet away from the wall? Assume a negative value means down.

    -3/4 ft/sec
    -4/3 ft/sec
    -5/4 ft/sec
    -4/5 ft/sec
    -1 ft/sec

7. If 2 + xy = 10, and dx/dt = -2, what is dy/dt when x = 2?

    -1
    0
    1
    2
    4

8. Find the limit as x approaches negative infinity of sin(ex)

    -1
    0
    1
    negative infinity
    the limit does NOT exist

9. Find the inverse of (2 + 5x)1/2, where x >= 0.

    (5/2) * (2 + 5x)-1/2
    (5 - 2x)2
    (x2 - 2)/5
    (x2 + 2)/5
    (x2 - 5)/2

10. Solve for x: ln(x3) = 2 * ln(8) - 3 * ln(2)

    0
    1
    2
    3
    4