14. Let f(x)=sin(1). (a) Sketch a clearly labeled graph of f(x), using a 1-1 scale. (12.1...

 

 

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14. Let f(x)=sin(1). (a) Sketch a clearly labeled graph of f(x), using a 1-1 scale. (12.1\ + + 31 2 (b) Explain why the slope of the tangent line to the graph of at the origin (x = 0) is given by the limit Sin (x) sin x lim 20 I X lim Sin Y X-0 (c) Approximate the limit using a table of values. X5 .5 3 +2 Siny X 0.959 0985 0.993 getting Closer to (d) Use your result in (c) to find an equation for the tangent line to f at the origin, and add a graph of it to your sketch in (a). 14. Let f(x)=sin(1). (a) Sketch a clearly labeled graph of f(x), using a 1-1 scale. (12.1\ + + 31 2 (b) Explain why the slope of the tangent line to the graph of at the origin (x = 0) is given by the limit Sin (x) sin x lim 20 I X lim Sin Y X-0 (c) Approximate the limit using a table of values. X5 .5 3 +2 Siny X 0.959 0985 0.993 getting Closer to (d) Use your result in (c) to find an equation for the tangent line to f at the origin, and add a graph of it to your sketch in (a).