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Questions and Answers
What is required for full credit on the midterm exam?
What is required for full credit on the midterm exam?
What is the maximum score possible on the midterm exam?
What is the maximum score possible on the midterm exam?
Which topics marked with a star (*) are considered the most important for the exam?
Which topics marked with a star (*) are considered the most important for the exam?
Which method should NOT be used to calculate values of sin, cos, and tan for the exam?
Which method should NOT be used to calculate values of sin, cos, and tan for the exam?
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What does the exam require regarding the application of the Intermediate Value Theorem?
What does the exam require regarding the application of the Intermediate Value Theorem?
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Which of the following best describes how limits will be addressed in the exam?
Which of the following best describes how limits will be addressed in the exam?
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When graphing functions, what properties are essential to recognize?
When graphing functions, what properties are essential to recognize?
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Which of the following is an improper use of differentiation rules on the exam?
Which of the following is an improper use of differentiation rules on the exam?
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What is the primary focus of Parts 1-3 in the proof outlined?
What is the primary focus of Parts 1-3 in the proof outlined?
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What does the equation $f(x+h)g(x+h) - f(x)g(x)$ represent?
What does the equation $f(x+h)g(x+h) - f(x)g(x)$ represent?
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Which operation is necessary to arrive at the Product Rule from the given formula?
Which operation is necessary to arrive at the Product Rule from the given formula?
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Which point represents the value of $g(0)$ in the unit circle equation $x^2 + y^2 = 1$?
Which point represents the value of $g(0)$ in the unit circle equation $x^2 + y^2 = 1$?
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In the area representation, which expression describes the part of the area that is equal to $f(x+h) - f(x)$?
In the area representation, which expression describes the part of the area that is equal to $f(x+h) - f(x)$?
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What is indicated by the limit $ ext{lim}_{h→0} rac{ ext{sin}(h)}{h}$?
What is indicated by the limit $ ext{lim}_{h→0} rac{ ext{sin}(h)}{h}$?
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How should coordinates for points A, B, and D be determined?
How should coordinates for points A, B, and D be determined?
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Which of the following expressions is equal to $f(x+h)g(x+h) - f(x)g(x)$?
Which of the following expressions is equal to $f(x+h)g(x+h) - f(x)g(x)$?
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Study Notes
Calculus I Midterm Review
- The midterm will cover topics from Calculus I, specifically focusing on limits, continuity, differentiability, and derivatives.
- You will need to be able to find the values of trigonometric functions like sine, cosine, and tangent at common angles.
- You should be able to determine the existence and values of both finite and infinite limits using algebraic methods.
- You will also need to be able to recognize if a limit exists as x approaches infinity and find its value if possible.
- Determining the continuity or differentiability of functions from formulas and graphs, as well as vice versa, is crucial.
- The Squeeze Theorem for limits and the Intermediate Value Theorem for continuous functions will be tested.
- You must be able to find derivatives using the limit definition and various differentiation rules (including implicit differentiation).
- Using derivatives to compute tangent line equations is another essential skill.
- You need to be able to estimate derivatives and average rates of change from formulas, graphs, and numerical data.
- Being able to graph the derivative of a function, given its original graph, and vice versa, will be examined.
- You will need to understand the main steps involved in the proof of the Product Rule, including how to find the formula for f(x+h)g(x+h) - f(x)g(x).
- You will need to be able to explain how to find the limit of sin(h)/h as h approaches 0 using a diagram with the unit circle.
- You should be able to understand the steps involved in calculating the limit of sin(h)/h as h approaches 0.
- The exam is worth 66 points and will be graded out of 60.
- You will obtain the most points for demonstrating computational skills (94%).
- The theoretical section covers the Product Rule and the limit of sin(h)/h as h approaches 0, these are worth 16% of the points.
- You will be given a choice of topics to answer from the theoretical section, but you must answer one question from each section (1-3 or 4-6).
- No calculators or electronic devices are allowed during the exam.
- You are allowed to use a single 3" x 5" index card as an aid during the exam.
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Description
Prepare for your Calculus I midterm by reviewing essential topics such as limits, continuity, differentiability, and derivatives. This quiz will test your skills in finding trigonometric function values, determining limits, and applying the Squeeze and Intermediate Value Theorems. Make sure you are ready to compute derivatives and tangent line equations!
