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# P07 - Project 7 MAC 2311 4 x x 1 Write the domain of f(x =...

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Project 7 MAC 2311 1. Write the domain of f ( x ) = 4 x - x x - 2 - 8 x . Rewrite f ( x ) as a simplified rational function in lowest terms, including restrictions on the domain. Then, use a number line to find the intervals on which f ( x ) is positive and those on which it is negative. This is one way to distinguish between limits that are or -∞ . Evaluate the following limits, and graph f ( x ) on the axes below. lim x →- 2 - f ( x ) = lim x →- 2 + f ( x ) = lim x 0 - f ( x ) = lim x 0 + f ( x ) = lim x 4 - f ( x ) = lim x 4 + f ( x ) = Hint: Be mindful of your domain (watch for holes), and use shifting, reflecting, etc. along with the fact that x + b x + a = x + a x + a + b - a x + a = 1 + b - a x + a 2. If possible, find the value of the constant c so that lim x 2 h ( x ) exists for the piecewise-defined function below. h ( x ) = x 2 - 4 | x 2 - 2 x | x < 2 x + cx 2 x > 2 What is lim x 0 h ( x ) ?

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3. In the theory of relativity, the mass m of a particle with speed v is: ( * ) m = m o p 1 - ( v/c ) 2 , where m o is the rest mass of the particle and c is the speed of light in a vacuum.
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P07 - Project 7 MAC 2311 4 x x 1 Write the domain of f(x =...

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