AboutPaul Klarreich Expertise I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
Expert: Paul Klarreich Date: 5/16/2008 Subject: Functions and polynomials.
Question I was wondering if you could help me with a few pre-calc problems that i just
can't seem to get down... the concept to me is more important than the
answers.
1. Given F(X) = [(x-2)(x^2-6x+10)] ÷ 2-x
A) find all points of discontinuity
B) specify the end behavior of F(X) as x approaches infinity and negative
infinity.
C) find the x- and y- intercepts of F(X)
D) Sketch the Graph of F(x)
2. Find all rational irrational and complex zeros : P(x)= 2x^5 + 5x^4-
8x^3-14x^2+6x+9
3. Air pressure (P) decreases exponentially with the height of (h) in meters
above the sea level:
P = P0e^-.00012h where P0 is the air pressure at sea level.
A) at the top of Mount Mckinley, height 6198 meters, what is the air pressure,
as a percent of the pressure at sea level?
B) The maximum cruising altitude of an ordinary jet is around 12,000 meters.
At that height, what si the air pressure, as a percent of the sea pressure at
sea level
Thanks!
Answer Questioner: Luke
Category: Advanced Math
Private: No
Subject: Pre-Calculus
Question: I was wondering if you could help me with a few pre-calc problems that i just
can't seem to get down... the concept to me is more important than the
answers.
>> Good, because this is a lot of questions.
1. Given F(X) = [(x-2)(x^2-6x+10)] ÷ 2-x
A) find all points of discontinuity
>> look for values of x where the denominator becomes zero. THEN you can divide out the (x-2)/(2-x), which gives you a factor of (-1). Since it divided out, you have a HOLE at x = 2.
Now your function is -(x^2-6x+10)
........................
B) specify the end behavior of F(X) as x approaches (POSITIVE?) infinity and negative infinity.
>> Look only at the first term: - x^2. Goes down at both ends, right?
......................
C) find the x- and y- intercepts of F(X)
>> x-int: Solve F(x) = 0. [Sorry, you won't get any in this case.]
>> y-int: Let x = 0.
............................
D) Sketch the Graph of F(x)
>> Looks like an inverted parabola, with that hole.
======================================================
2. Find all rational irrational and complex zeros :
P(x)= 2x^5 + 5x^4 - 8x^3 - 14x^2 + 6x + 9
>>>>
Try x = +-1, +-3, +-9, and x = +-1/2, +-3/2, +-9/2
When one works, divide out (x - it).
Then start over with the quotient. If all goes (very) well, you get down to a quadratic. Solve that with whatever is right.
You might also get lucky and find a tricky way to factor.
See you next month.
..........................................
3. Air pressure (P) decreases exponentially with the height of (h) in meters
above the sea level:
P = P0e^-.00012h where P0 is the air pressure at sea level.
A) at the top of Mount Mckinley, height 6198 meters, what is the air pressure,
as a percent of the pressure at sea level?
>> Let h = 6198, use your calculator. The e^-..... part is your percentage. [Convert to a percent, of course.]
B) The maximum cruising altitude of an ordinary jet is around 12,000 meters.
At that height, what is the air pressure, as a percent of the sea pressure at
sea level
