1) Find the domain and range of the rational function y( x) = x^2-25 / 2x^2 + 13x+15
A) Factor the numerator and denominator
B) Determine the point of discontinuity if it exists.
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Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&... Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&-2&0)],Vector_4=[Column(1&-2&-2)].
Show that S={Vector_1,Vector_2,Vector_3,Vector_4} is linearly dependent.
Show that Vector_3 can be written as a linear combination of Vector_1,Vector_2 and Vector_4.
Show that T={Vector_1,Vector_2,Vector_4} is linearly independent.
Show that the set of all linear combinations of vectors from S is the same as the set of all linear combinations of vectors from T.
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Through the midpoint of each side of a triangle,a line is drawn parallel to the bisector of the opposite angle. Prove that these three lines are concurrent and that the point of concurrency is collinear with the centroid and the incenter of the triangel. (hint :use dilation)
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Estimate the area A between the graph of the function f(x)=
square root of x and the interval [0,49]. Use an approximation
scheme with n=2,5, and 10 rectangles. Use the right
endpoints.
Round your answers to three decimal places.
A2=
A5=
A10=
| Click |
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Land vs. Water Heating Differences. Refer to pgs. 114-115 of your text and notes from Unit 4 Lecture. In addition to the seasons, latitudinal differences, and altitude, a location’s proximity to a large water body may have a strong affect on temperature. We refer to this as the “marine” or “maritime” effect. In contrast, a large landmass with little marine influence has the opposite effect on temperature and is said to be “continental.”
1. List four reasons why water bodies do not heat up or cool down as much as continental areas of similar latitude. a. _____________________________________________ b. ______________________________________________ c. _______________________________________________ d. ________________________________________________
Daily Cycle of Temperature. Refer to pg. 95 of your text along with your notes from lecture 4.
2. At what time of day does maximum insolation normally occur?
3. The maximum daily temperature generally lags behind the time of maximum insolation. Why? Explain your answer in terms of net radiation.
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Determine the intervals on which the function below is increasing or decreasing, concave or convex. Determine also relative maxima and minima, inflections points, symmetry, asymptotes, and intercepts if any. Then sketch the curve.
. ? = 3?+3/(3? − 3)^2
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Let AB be a diameter of a circle and suppose that UV is a perpendicular chord. Show that cr(A,U,B,V)=2
(where cr = cross-ratio)
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Construct expansions in a two-individual universe of discourse for the following sentence:
(x) [Fx --> (Gx v Hx)]
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A circular puddle is expanding. How quickly is the radius
changing when the area is 50 square centimeters and the area is
increasing by 4 square centimeters per second?
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Explain what the Gaussian elimination does, by column picture, to a linear system with 3 unknowns and 3 equations.
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An open-top rectangular box has a volume of 250 cm 3. The width of the box is 5 cm. The cost is $2/ cm 2 for the base and $1/ cm 2 for the other sides. What is the minimum cost for making the box?
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Consider the following function. (If an answer does not exist, enter DNE.) f(x) = ln(8 − ln(x))
(a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.)
x =
Find the horizontal asymptote(s). (Enter your answers as a
comma-separated list.)
y =
(b) Find the interval where the function is increasing. (Enter your
answer using interval notation.
Find the interval where the function is decreasing. (Enter your
answer using interval notation.
(c) Find the local maximum and minimum values.
| local maximum value | |
| local minimum value |
(d) Find the interval where the function is concave up. (Enter your
answer using interval notation.
Find the interval where the function is concave down. (Enter your
answer using interval notation.)
Find the inflection point.
(x, y) =
(e) Use the information from parts (a)-(d) to sketch the graph of f.
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f (x) = -0.248226*cos (2 x) - 0.0184829*cos ((2+2)x) - 0.0594608*cos(x)*sin(x) + 0.123626*sin ((2+2)x).
The intervall is ]0, 3/2[
What is the local maximum and local minimum? Answer with 5 decimals
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Suppose the response of a drug is modeled by the function ?(?) = ?2/ 3+?2 where ? is the drug concentration. At what drug concentration does the inflection point occur? Show that there is a change of concavity at that point.
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Consider rotations Rθ and Rα in R^2 . (a) From geometrical considerations, we know that Rα◦Rθ =Rα+θ. Verify the corresponding matrix equation. (b) Prove that [R−θ] T =[Rθ]
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