document.write( "Question 1000816: This is at the end of our chapter where we learned about arithmetic and geometric sequences and the binomial theorem. The question is: Expand the binomial in the difference quotient and simplify. I'm given [f(x+h)-f(x)] divided by h, I'm then given f(x)=x cubed. I don't get how this relates to series, sequences, their sums, or finding the Nth term, if you could explain the connection as well, I would appreciate it so much. \n" ); document.write( "

Algebra.Com's Answer #618143 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=x%5E3\"$
\n" ); document.write( " $\"f%28x%2Bh%29=%28x%2Bh%29%5E3\"$
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\n" ); document.write( "I do not see how this relates to series, sequences, their sums, or finding the Nth term either.
\n" ); document.write( "I see how this relates to algebra in general, and polynomials in particular, and
\n" ); document.write( "I see how this is a sneaky introduction to derivatives,
\n" ); document.write( "which would belong in an early calculus lesson.
\n" ); document.write( "If the name of your class is pre-calculus, a sneaky introduction to derivatives may be the purpose of this problem.
\n" ); document.write( " $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"$ is the slope of the line AB that passes through points
\n" ); document.write( " $\"A%28x%2Cf%28x%29%29\"$ and $\"B%28x%2Bh%2Cf%28x%2Bh%29%29\"$ of the graph of $\"f%28x%29\"$ .
\n" ); document.write( "As you decrease $\"abs%28h%29\"$ towards zero, points A and B get closer together,
\n" ); document.write( "\"tending to\" being the same point A, and the line AB tends to being the tangent to the curve at A.
\n" ); document.write( "The derivative of $\"f%28x%29\"$ is the function
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