Title Questions.pdf ✅

1. NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function is assumed to be the set of all real numbers for which is a real number. Let be the function defined above, where is a constant. (a) For what value of , if any, is continuous at ? Justify your answer. (b) What type of discontinuity does have at ? Give a reason for your answer. (c) Find all horizontal asymptotes to the graph of . Show the work that leads to your answer. AP CALCULUS AB Test Booklet Unit 1 - Limits and Continuity-FQR AP Calculus AB Page 1 of 9
2. NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function is assumed to be the set of all real numbers for which is a real number. Let be the function defined above, where is a constant. (a) For what value of , if any, is continuous at ? Justify your answer. (b) What type of discontinuity does have at ? Give a reason for your answer. (c) Find all horizontal asymptotes to the graph of . Show the work that leads to your answer. Test Booklet Unit 1 - Limits and Continuity-FQR Page 2 of 9 AP Calculus AB
3. NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function is assumed to be the set of all real numbers for which is a real number. Consider the differential equation d d . Let be the particular solution to the differential equation with the initial condition . (a) Write an equation for the line tangent to the graph of at . Use the tangent line to approximate . (b) Find the value of d d at the point . Is the graph of concave up or concave down at the point ? Give a reason for your answer. (c) Find , the particular solution to the differential equation with the initial condition . (d) For the particular solution found in part (c), find . Test Booklet Unit 1 - Limits and Continuity-FQR AP Calculus AB Page 3 of 9