One morning while flexing in front of the bathroom mirror, I realized my godlike build is a gift to mankind. I also realized my massive arms are geometrically perfect. To prove this, I graphed my bulging biceps on an x-y axis. As it turns out, I am perfectly y-symmetric. My elbows were at (-10,0) and (10,0) respectively and my hands were located at (-6,5) and (6,5). My biceps were off the charts so I decided not to graph them.

To help launch my body-building career, I post these problems on Mr. Kelley's web page to help you become more acquainted with my body. If you catch yourself drooling while working on this problem, please try and control yourself.        --Chris

Chris' arms are shown in red, a power color to be sure

    (a)    Find the domain and range of my arms.
    (b)    Calculate the lengths of my forearms.
    (c)    Find the angle at which my elbows are bent.
    (d)    Express answers to (c) in both radians and degrees.
    (e)    Create equations for both forearms.

Difficulty Rating: 

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Solution:     (a)        Domain: [-10,10] Range: [0,5]
    (b)        According to the distance formula, the length of each forearm is the square root of 41.
    (c)/(d)    In order to find this angle, look at the blue triangle on Chris' left forearm (your right): With this right triangle, you can get the angle two ways: or . Either answer gives you 51.34 degrees or .896 radians. Indicate the unit of measure.
    (e)    The slope of Chris' right forearm is found by using its endpoints: (-10,0) and (-6,5). The slope is 5/4. Similarly, his left arm has slope -5/4. Finally, using point-slope form, or slope-intercept form, the equations are y=(-5/4)x+25/2 and y=(5/4)x+25/2.

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Calculus II (BC): L'Hopital's Rule

Evaluate: .

Difficulty Rating:  Source: Calculus: Concepts and Contexts, James Stewart, p. 305.

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Solution: Because direct substitution leads to 0/0 (indeterminate form), we can utilize L'Hopital's Rule. In fact, as substitution at that point leads to indeterminate form again, we will apply L'Hopital two more times before we can substitute in to get 2/6 or 1/3. Remember that to take the derivative of (sec x)², we use the chain rule, first bringing down the two due to the power rule to get 2 (sec x)*(sec x)', and then taking the derivative of sec x.

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