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Asymptote

Calculus 1 Exam 3 3of4

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Calculus
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Geometry
Algebraic geometry
Conic sections
Analytic geometry
Hyperbola
Focus
Parabola
Ellipse
Semi-major and semi-minor axes
Degenerate conic
Degeneracy
Asymptote

14) Determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. 15) Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. a) b) Vertex: Focus: Directrix:

Ap Calc Test - First Semester

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Calculus
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Mathematical analysis
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Calculus
Differential calculus
Convex analysis
Convex function
Derivative
Limit of a function
Continuous function
Asymptote

AP Calculus AB ? Semester Exam Review No Calculator Portion A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: DO NOT WRITE ON THIS TEST. After examining the form of the choices, decide which is the best of the choices given and fill in the corresponding oval on the answer sheet. No partial credit will be given. Do not spend too much time on any one problem. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. 1. Let f(x) be the function whose graph is shown to the right: A. B. C. D. E. none of the above 2. The graph of f(x) is shown in the figure to the right. What is ? A. ?1 B. 1 C. 2 D. it varies E. does not exist

Limits

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Calculus
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Polynomial
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Rational function
Limit of a function
L'Hôpital's rule
Technology

Limits Number value that f(x) approaches as the values of x approach a specific numberIf f(x) is a polynomial or a rational function and a is in the domain of f(x), then Limits that fail to exist 1. If f(x) approaches a different number from the right than from the left: 2. If f(x) increases or decreases without bound as it approaches a number: 3. If f(x) oscillates between 2 fixed value One-sided limits If only approaching from the right If only approaching from the left Limit Existence Theorem = L iff = L = Vertical Asymptote If = or = Then x=a is a vertical asymptote Horizontal Asymptote If or Then y=b is a horizontal asymptote

Horizontal Asymptotes

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Algebra
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horizontal asymptotes

Horizontal asymptotes are horizontal lines the graph approaches. Finding horizontal asymptotes: If the degree, which is the largest exponent, of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). If the degree of the numerator is bigger than the denominator, a horizontal asymptote does not exist. (none) If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator ?
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