Tag Archives: Calculus

09.18.14
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Precalculus – Domain of a function

Q: What is the domain of this function?

 

Answer:

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Explanation:

The domain of a function is a description of the x-values that may be plugged into the function. For a square root function, the restriction is that the number under the radical must not be negative. Therefore,

 

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09.12.14
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ACT, Geometry – diagonal of a rectangular prism

Q: What is the (straight-line) distance between points A and B on the figure below?

rectangularprism2

Answer:  7

Explanation:  We are finding the length of the green segment below:

 

rectangularprism2wline

This requires the three-dimensional version of the distance formula:

  2014-09-12_225150

There is another way to do this, using a progression of two right triangles, with the green segment being the hypotenuse of the second triangle, but I find the above formula much simpler.  It is just an extension of the ‘usual’ (2-dimensional) distance formula we are so familiar with from Algebra and Geometry.

BUT if you want an even easier way, and I know you do, use my TI-84 Plus program ‘DIST3D’.

 

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09.10.14
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Calculus – Limits

Q: Find the limit:

Answer: -5

Explanation: Direct substitution (plugging in -1) yields 0/0, an indeterminate form. Factor and cancel:

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09.10.14
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Precalculus – logarithms

Q: Solve the following equation involving logarithms:

Answer: x=4

Explanation:

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