Limits
Exponential Functions
Trig Functions
Logarithms
Miscellaneous
100
Find the values for the following limits on the graph provided a. limit as x approaches -2 b. limit as x approaches 0 c. limit as x approaches 2 d. limit as x approaches 4
What is a. 0 b. 7 c. DNE d. 8
100
For the following problems, state the initial quantity and the growth rate in percentage. Is the growth rate continuous? a. P=5(1.07)^t b. P=3.2e^(0.03t) c. P=15e^(-0.06t)
What is a. initial value: 5, growing 7%, not continuous b. initial value: 3.2, growing 3%, continuous c. initial value: 15, decaying 6%, continuous
100
what is the formula for sinusoidal functions? Explain what each variable means and how to find it.
What is f(t) = Asin(Bt) + C f(t) = Acos(Bt) + C
100
How would you simplify ln(A/B)?
What is ln(A) - ln(B)
100
What are the different kinds of discontinuities?
What is breaks, jumps, holes, asymptotes
200
explain what it means for the limit to approach from the right? from the left?
What is examining a pattern in the values a little above x examining a pattern in the values a little below x
200
A population P grows at a continuous rate of 2% a year and starts at one million. a. find the formula b. what is the population after 130 years (round to one decimal place)
What is a. P = 1e^(0.02t) b. 13.5 million
200
Consider y = 5 + cos(3x) a. what is it's amplitude? b. What is it's period? c. sketch it's graph
What is a. A = 1 b. 2(pi)/3
200
Put the function P= 174(0.9)^t in the form P=Poe^(kt) Leave your answer in exact form.
What is P=174e^(ln(0.9)t)
200
Are the following functions continuous for all x? a. f(x) = 1/x b. f(x) = abs(x)/x for x not equal to 0 0 when x = 0 c. f(x) = x/x when x not equal to 0 1 when x=0 d. f(x) = 2x/x when x not equal to 0 3 when x=0
What is a. no b. no c. yes d. no
300
Find the value of k so that the limit exists lim as x approaches -2 of (x^2 + 4x + k)/(x+2)
What is k= 4
300
Find the exponential formula going through the points (1,6) and (2,18)
What is P=2(3^t)
300
find the formula for the graph provided
What is y = 2sin(x/4) + 2
300
If h(x) = ln(x+a) where a>0, what is the effect of increasing a on a. the y-intercept? b. the x-intercept?
What is a. if a increasing, the y-intercept increases b. increasing a moves the x intercept to the left
300
find the x and y intercepts of (x^2 - 1) / (x^2 + 4x +4). What kind of function is this?
What is Rational function x-intercept: x=1, -1 y-intercept: y=-1/4
400
find the limit as x approaches 0 of (2^x - 1)/x
What is 1
400
During 1988 Kenya's inflation rate averaged 0.67% a day. This means that, on average, prices went up by 0.67% from one day to the next. a. By what percentage did prices in Kenya increase in June 1988? Round to one decimal place b. What was Kenya's annual inflation rate during 1988? Round your answer to one decimal place.
What is a. 47.3% b. 11199.4%
400
The Bay of Fundy in Canada has the largest tides in the world. The difference between low and high water levels is 15 meters (nearly 50 feet). At a particular point the depth of the water, meters, is given as a function of time, , in hours since midnight by y = D + Acos(B(t-C)) a. what is the physical meaning of D? b. What is the value of A? c. What is the value of B assuming that the time between high tides is 12.4 hours d. what is the physical meaning of C?
What is a. the average depth of water b. 7.5 meters c. 2 *(pi/12.4) d. the time of high tide
400
The size of an exponentially growing bacteria colony doubles in 5 hours. How long will it take to triple?
What is 7.925 hours
400
An air freshener starts with 30 grams and evaporates. a. Write the formula for the quantity Q in grams remaining after t days if the 2 grams evaporate each day. b. How long will it take for all 30 grams to evaporate? c. Is this realistic? What would be better?
What is a. y = 30 - 2x b. 15 days c. exponential function would be more accurate.
500
Determine the end behavior of each function as x approaches (1) infinity and (2)negative infinity a. f(x) = x^7 b. f(x) = 3x + 7x^3 - 12x^4 c. f(x) = x^-4 d. f(x) = (6x^3 - 5x^2 +2)/(x^3-8)
What is a. (1) f(x) approaches infinity (2) f(x) approaches negative infinity b. (1) f(x) approaches negative infinity (2) f(x) approaches negative infinity c. (1) f(x) approaches 0 (2) f(x) approaches 0 d. (1) f(x) approaches 6 (2) f(x) approaches 6
500
In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear weapons and got into the bones of people alive at the time. If the half-life of strontium-90 is 29 years, what fraction of the strontium-90 absorbed in 1960 remained in the people's bones in 1990?
What is 48.8%
500
A population of animals oscillates sinusoidally between a low of 700 on January 1 and a high of 900 on July 1. Find a formula for the population as a function of time in months since the start of the year
What is P = 800 - 100cos(pi/6 * t)
500
A cup of coffee contains 100 mg of caffeine which leaves the body at a continuous rate of 17% per hour. a. write a formula for the amount, A mg, of caffeine in the body t hours after drinking a cup of coffee. b. what is the half life of caffeine?
What is a. A=100e^(-0.17t) b. 4.077 hours
500
Let f(x) = x^2 + 3(x) + 5 and g(x) = x^2 + 7. a. find g(f(x)) b. find f(g(x)) c. find f(h-2) - f(7)
What is a. x^4 + 3^3 + 13x^2 + 42x + 32 b. x^4 + 17x^2 + 75 c. h^2 + h + 79
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