Test your understanding of a tangent line as the limit of secant slopes.

Problem

Consider the graph of f and complete the table below.
Left Sideequals, comma, is less than or is greater thanRight Side
start fraction, f, left parenthesis, 0, right parenthesis, minus, f, left parenthesis, minus, 2, right parenthesis, divided by, 2, end fraction, space
1
limx1f(x)f(1)x+1 \displaystyle \lim_{x\,\to\,-1} \dfrac{f(x)-f(-1)}{x+1}\
limx1f(x)f(1)x1 \displaystyle \lim_{x\,\to\,1} \dfrac{f(x)-f(1)}{x-1}\
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