Refer to Example 1.
(a) Find an equation of the tangent line to the curve that is parallel to the secant line AD.
(b) Use part (a) to show that ln 2 > 0.66.
(a) By comparing areas, show that .
(b) Use the Midpoint Rule with n= 10 to estimate the value of ln 2.
To find: An equation of the tangent line to the curve .
From Example 1 the inequality is .
The natural logarithm is defined as .
Hence, the function is from the limits 1 to 2 as x takes the value from 1 to 2.
Choose two points and as 1 and 2 respectively. Their corresponding y coordinate is as follows.
When is 1, then and when is 2, then .
The slope of the curve is obtain from the point and .
Calculate the derivat
To show: The value of .
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