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Page "Curve sketching" ¶ 7
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Determine and curve
* Determine the x and y intercepts of the curve.
* Determine the symmetry of the curve.

Determine and .
Determine the average per capita income for the U. S. based on the last three years.
Determine the ratio of 50% to the average per capita income of the U. S. ( Divide 50 by the result obtained in item 2 above.
Determine for each State ( except the Virgin Islands, Guam and Puerto Rico, and, prior to 1962, Alaska and Hawaii ) that percentage which bears the same ratio to 50% as the particular State's average per capita income bears to the average per capita income of the U. S..
Determine the particular State's `` allotment percentage ''.
Determine each State's population.
Determine the sum of the products obtained in item 8 above, for all the States.
Determine the ratio that the amount being allotted is to the sum of the products for all the States.
Determine the particular State's unadjusted allotment for the particular fiscal year.
Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is greater than its maximum allotment, and if so lower its unadjusted allotment to its maximum allotment.
Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is less than its minimum ( base ) allotment, and if so raise its unadjusted allotment to its minimum allotment.
Determine the average per capita income for the United States for the last three years.
Determine the ratio of 40% to the average per capita income of the United States.
Determine for each State ( except the Virgin Islands, Guam, Puerto Rico, and, prior to 1962, Alaska and Hawaii ), that percentage which bears the same ration to 40% as the particular State's average per capita income bears to the average per capita income of the United States.
Determine the particular State's `` Federal Share ''.
Determine how much topography limits useful area or what the costs of earth moving or grading might be.
3 ) Determine necessary soil parameters through field and lab testing ( e. g., consolidation test, triaxial shear test, vane shear test, standard penetration test );
Determine if elevating the legs makes the swelling go away.
# Determine the type of training examples.
# Determine the input feature representation of the learned function.
# Determine the structure of the learned function and corresponding learning algorithm.
* Parsing: Determine the parse tree ( grammatical analysis ) of a given sentence.
* Diagnosis: Determine a diagnosis that guides future patient / client management.
* Prognosis: Determine patient / client prognoses.
* Determine the defuzzification method.
Determine the area and cross sectional velocity for each supply or exhaust grill in the room.

asymptotes and curve
More generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.
Thus, both the x and y-axes are asymptotes of the curve.
Oblique asymptotes are diagonal lines so that the difference between the curve and the line approaches 0 as x tends to +∞ or −∞.
In this case, the curve has vertical asymptotes and this limits the span to πc.
In the case of the curve the asymptotes are the two coordinate axes.
* draw a smooth curve through those points using the straight lines as asymptotes ( lines which the curve approaches ).
Also determine from which side the curve approaches the asymptotes and where the asymptotes intersect the curve.
The curve has two more asymptotes, in the plane with complex coordinates, given by

asymptotes and .
There are potentially three kinds of asymptotes: horizontal, vertical and oblique asymptotes.
For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.
Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph.
The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.
The x and y-axes are the asymptotes.
The asymptotes most commonly encountered in the study of calculus are of curves of the form.
These can be computed using limits and classified into horizontal, vertical and oblique asymptotes depending on its orientation.
Vertical asymptotes are vertical lines ( perpendicular to the x-axis ) near which the function grows without bound.
More general type of asymptotes can be defined in this case.
The graph of a function can have two horizontal asymptotes.
Horizontal asymptotes are horizontal lines that the graph of the function approaches as.
Functions may lack horizontal asymptotes on either or both sides, or may have one horizontal asymptote that is the same in both directions.
In the graph of, the y-axis ( x = 0 ) and the line y = x are both asymptotes.
A rational function has at most one horizontal asymptote or oblique ( slant ) asymptote, and possibly many vertical asymptotes.
The degree of the numerator and degree of the denominator determine whether or not there are any horizontal or oblique asymptotes.
There are therefore two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch.
The asymptotes of the hyperbola ( red curves ) are shown as blue dashed lines and intersect at the center of the hyperbola, C. The two focal points are labeled F < sub > 1 </ sub > and F < sub > 2 </ sub >, and the thin black line joining them is the transverse axis.
So the parameters are: a — distance from center C to either vertex b — length of a perpendicular segment from each vertex to the asymptotes c — distance from center C to either Focus point, F < sub > 1 </ sub > and F < sub > 2 </ sub >, and θ — angle formed by each asymptote with the transverse axis.

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