b) Create a table that numerically represents the value of this limit from the left: lim...

 

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b) Create a table that numerically represents the value of this limit from the left: lim h0- h 2xh+ h h Describe the pattern that is revealed using this numerical method? Using this pattern, what does this f(x+h)-f(x)? suggest is the value of the left-sided limit, lim h0- h (x+h)-f(x)? h -0.1 -0.01 x = -1 c) Using the numerical evidence, what would you guess is the value of the two-sided limit, lim h0 x=0 d) As is most often the case when finding the derivative of a function, the result is another function rather than a number. The usefulness of this function is it allows us, in this case, to plug in various x- values to find the slope of the lines tangent to f(x) = x. Using the result from part (c), find the slope of the tangent lines at x = -1, x = 0, and x = 3. (See graphs below). Describe how the answers relate to the graphs of the tangent lines below. 8 7 64 f(x+h)-f(x) h -0.001 5 -0.0001 4 x = 3 7 b) Create a table that numerically represents the value of this limit from the left: lim h0- h 2xh+ h h Describe the pattern that is revealed using this numerical method? Using this pattern, what does this f(x+h)-f(x)? suggest is the value of the left-sided limit, lim h0- h (x+h)-f(x)? h -0.1 -0.01 x = -1 c) Using the numerical evidence, what would you guess is the value of the two-sided limit, lim h0 x=0 d) As is most often the case when finding the derivative of a function, the result is another function rather than a number. The usefulness of this function is it allows us, in this case, to plug in various x- values to find the slope of the lines tangent to f(x) = x. Using the result from part (c), find the slope of the tangent lines at x = -1, x = 0, and x = 3. (See graphs below). Describe how the answers relate to the graphs of the tangent lines below. 8 7 64 f(x+h)-f(x) h -0.001 5 -0.0001 4 x = 3 7