Provide an appropriate response.Explain why the Trapezoidal Rule gives an exact value for the integral 
What will be an ideal response?
The error for the Trapezoidal Rule satisfies 
? 
, where M is an upper bound on the second derivative of f(x) on the interval [a, b].
In this case f(x) = 3x - 7. Since f(x) is a linear function, f"(x) = 0 for all x. So 
? 0, or 
= 0. Therefore, the Trapezoidal Rule gives the integral's exact value. This makes sense because for a linear function, the trapezoids fit the graph perfectly.
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Evaluate the integral.
A. 
tan34t - tan 4t + t + C
B. 
tan34t - 
tan24t + 
tan 4t + t + C
C. - 
tan34t + 
tan 4t + C
D. 
tan34t - 
tan 4t + t + C
Solve the problem.The rates of death (in number of deaths per 100,000 population) for 1-4 year olds in the United States between 1980-1995 are given below. (Source: NCHS Data Warehouse) 
A logarithmic equation that models this data is y = 822.99 - 167.55 ln x where x represents the number of years since 1900. Use this equation to predict the rate of death for 1-4 year olds in 2005.
What will be an ideal response?
Perform the indicated operations and simplify the result. Leave the answer in factored form.
+ 
A. 
B. 
C. 
D. 
Solve the problem.A rectangular patio has dimensions 10 feet by 15 feet. The patio is surrounded by a border with a uniform width of 4 feet. Find the area of the border.
A. 136 ft2 B. 264 ft2 C. 166 ft2 D. 116 ft2