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1.Verify the identity. Show your work.
cot Î¸ âˆ™ sec Î¸ csc Î¸
2.A gas company has the following rate schedule for natural gas usage in single-family residences:
Monthly service charge $8.80
Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms $0.85870/therm
What is the charge for using 25 therms in one month? Show your work.
What is the charge for using 45 therms in one month? Show your work.
Construct a function that gives the monthly charge C for x therms of gas.
3.Complete the following:
(a) Use the Leading Coefficient Test to determine the graph’s end behavior.
(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.
(c) Find the y-intercept. Show your work.
f(x) x2(x + 2)
4.Verify the identity. Show your work.
(1 + tan2u)(1 – sin2u) 1
5.Verify the identity. Show your work.
cot2x + csc2x 2csc2x – 1
6.Verify the identity. Show your work.
1 + sec2xsin2x sec2x
7.Verify the identity. Show your work.
cos(Î± – Î²) – cos(Î± + Î²) 2 sin Î± sin Î²
8.Find the vertical asymptotes, if any, of the graph of the rational function. Show your work.
9.The formula A 118e0.024t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand? Show your work.
10.Find the specified vector or scalar. Show your work.
u -4i + 1j and v 4i + 1j; Find .||u+v||.
11.Find the exact value of the trigonometric function. Do not use a calculator.
12.Find the x-intercepts (if any) for the graph of the quadratic function.
6x2 + 12x + 5 0
Give your answers in exact form. Show your work.
13.Use the compound interest formulas A Pert and A P(1+r/n)^nt to solve.
Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually? Show your work.
14.Find functions f and g so that h(x) (f âˆ˜ g)(x).
h(x) (6x – 14)8
15.Begin by graphing the standard absolute value function f(x) | x |. Then use transformations of this graph to describe the graph the given function.
h(x) 2 | x | + 2
16.Find the reference angle for the given angle. Show your work.
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