The table below shows values of a function \(f(x)\).  Use Trapezoid Rule with four equal subintervals (\(n=4\)) to estimate the value of the integral \ 

Suppose the cost of utilities for a house is given by \ where \(t\) is in months. Find the average cost of utilities from December (\(t=0\)) to June (\(t=6\)).

Evaluate the integral, if it exists.\

Find the equation of the tangent line to the curve \ at the point \(\displaystyle x = \frac{1}{2}\).

Order: Omeprazole 11mg, gastrostomy tube, every 12 hours, for reflux  Child’s weight: 22 kg Safe dose range: 1-1.5mg/kg/day in two divided doses   a) What is the safe low dose (mg/dose) for this child? b) What is the safe high dose (mg/dose) for this child?  c) Is the ordered dose safe for this child?

Find the total mass of the \(1\) m rod whose linear density function is given by \ for \(0 \leq x \leq 1\).

Which of the following is the partial fractions decomposition of the rational function \

Order: Vancomycin 600mg, intravenously, every 6 hours, for moderate infection  Child’s weight: 50 kg  Safe dose range: 10-15mg/kg/dose (max dose 750mg) every 6 hours    a) What is the safe low dose (mg/dose) for this child?  b) What is the safe high dose (mg/dose) for this child? c) Is the ordered dose safe for this child?  

Evaluate the indefinite integral \ (Hint: Integration by Parts.)

Evaluate the integral \(Hint: \(\sin^2{x}+\cos^2{x}=1\))