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Limit of a function

Ap Calc Test - First Semester

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Calculus
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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 AND CONTINUITY

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Limits and Continuity Brief Review Limit ? intended height (y-value) of the function. Properties: add, subtract, divide, multiply, multiply constant and raise to any power. Techniques to Evaluation: Direct Substitution ? plug the x-value in?if you get a number you are done?if you get an indeterminate form?. 1.) Try to factor the expression. Cancel common factors and try direct substitution again. 2.) Try tables or graphs?.try plugging in a number close to the x-value to the right and the left. 2. 3. 4. 5. 6 7. 8.

Limits

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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
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