Provide an appropriate response.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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Use the rules for exponents to rewrite the expression and then evaluate the new expression. 42 ? 45
A. 262,144 B. 16,777,216 C. 16,384 D. 1,048,576
Provide an appropriate response.Determine which of the following is used to solve the inequality 
> c, for c > 0.
A. ax + b > c and ax + b < -c B. ax + b < c and ax + b > -c C. ax + b > c or ax + b > -c D. ax + b > c or ax + b < -c
Graph the solution set to the given system of inequalities.x ? 0, y ? 02x + y ? 6x + 2y ? 6
A. 
B. 
C. 
D. 
Provide an appropriate response.Solve the system: 
What will be an ideal response?