indigoelk609

Cal III can i get help

4. Given f(x)=   f'(x)=  f"(x)= 

a) Provide a complete analysis of f(x) and complete the passage. Show all your work in the space provided below.

“f(x) has x-intercept(s) of __________ and y-intercept of __________. It has two types of asymptotes: one type is _______________ asymptote(s) at __________________ and the other type is _______________ asymptote(s) at __________________. f(x) decreases for
____________________________________ and has (how many?) _____________ local extrema. The graph concaves up for ____________________________and concaves down for ____________________________. The point(s) of inflection is at ___________. The domain of f(x) is _______________________ and the range is _______________________”

b) State the asymptotic and end behaviours.

c) Use the information to sketch f(x).

A bird is foraging for berries.  If it stays too long in any one patch it will be spending valuable foraging time looking for the hidden berries, but when it leaves it will have to spend time finding another patch. A model for the net amount of food energy in joules the bird gets if it spends t minutes in a patch is E= 3000tt+4 . Suppose the bird takes 2 min on average to find each new patch, and spends negligible energy doing so. How long should the bird spend in a patch to maximize its average rate of energy gain over the time spent flying to a patch and foraging in it?   Compare numeric, graphical, and algebraic strategies to solve this problem.

Figure below shows a pressurized tank, in which the pressure of the gas must be maintained at 350 psi. Explain the role of each process control element in the feedback system when the pressure suddenly drops below the setpoint.

Given f(x)=   , find the absolute extrema of f(x) for −9 ≤ x ≤ 5 

A bandpass filter passes signals with frequencies that are within a certain range.In this filter the ratio of the magnitudes of the voltages is given by:
RV=V0/Vi=wRC/sqrt(1-w^2LC)^2+(wRC)^2 where w is the frequency of the input signal.Given R=1000ohm,L=11mH and C=8µF,determine the frequency range that corresponds to RV>=0.87.
Using MATLAB:
a) First plot the graph
b)Use matlab to construct a script for the Bisection method and Newton's method to find one of the possible roots.

Propane (C3H8) is burned with excess air to ensure complete combustion. If 55 kg of CO2 and 15 kg of CO are obtained when propane is completely burned with 500 kg of air, determine the following:

1. Mass of propane burnt.
2. Percent excess air.
3. Composition of product gas.

Reactions are :     C3H8 + 5 O2→ 3 CO2 + 4 H2O

                             C3H8 + 3.5 O2→ 3 CO+ 4 H2O

MWair=29 kg/kmol

Atomic Masses: C:12, H:1, O:16