Solve the problem.Consider the functions f(x) = x2 and g(x) = x3 and their linearizations at the origin. Over some interval 
the approximation error for g(x) is less than the approximation error for f(x) for all x within the interval. Derive a reasonable approximation for the value of ?. Show your work. (Hint, the absolute value of the second derivative of each function gives a measure of how quickly the slopes of the function and its linear approximation are deviating from one another.)
What will be an ideal response?
? ? 
. The slopes of g(x) and its linear approximation are deviating from each other more slowly than the slopes of the corresponding curves for f(x) as long as
Since 
and 
then 
or 
Thus, 
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Solve the problem.In a study of 135 women, roughly half took estrogen as well as calcium and vitamin D supplements and received regular dental checkups. The remaining women received the supplements and the checkups but substituted a sugar pill for the estrogen. Those who received the estrogen had an average 3.6 percent gain in bone density compared to a 0.2 percent bone density improvement in those taking the sugar pill. This study can best be described as
A. a survey using quota sampling. B. a controlled placebo experiment. C. a census. D. a survey using simple random sampling. E. the placebo effect.
Graph the function.f(x) = 
A. 
B. 
C. 
D. 
Find the distance between the pair of points. Where appropriate, give an approximation to three decimal places.
and 
A. 
? 0.373
B. 
? 0.656
C. 
? 0.636
D. 
? 7.655
Compute each expression and compare.52 + 32; (5 + 3)2
A. 34; 16; sum of squares is greater than square of sum B. 34; 64; square of sum is greater than sum of squares C. 16; 64; square of sum is greater than sum of squares D. 16; 16; both are equal