Given that the definite integral from to of equals , what is the value of the definite integral from to of ?
1. Limits and Continuity
Introduction to Limits
- Multiple Choice25views
- Multiple Choice
Given the double integral , which of the following represents the correct limits of integration after changing the order of integration?
6views - Textbook Question
Using the Formal Definition
Prove the limit statements in Exercises 37–50.
limx →4 (9 − x) = 5
149views - Textbook Question
Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist.
203views - Multiple Choice
Given the graph of the function below, on which interval is continuous?
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Which of the following regions in the plane has an area equal to the limit ? Do not evaluate the limit.
20views - Multiple Choice
Given the geometric series , find the sum of the series , where .
21views - Multiple Choice
Use the ratio test to determine whether the series converges or diverges.
25views - Multiple Choice
Given the graph of a function , find a number such that if , then .
21views - Multiple Choice
For the function , what is the average rate of change from to ?
4views - Textbook Question
Using the Formal Definition
Prove the limit statements in Exercises 37–50.
lim x→0 x sin (1/x) = 0
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169views - Multiple Choice
Which of the following statements about the series is true?
20views - Multiple Choice
Consider the function . Determine if has any points of discontinuity, and explain your reasoning.
27views - Textbook Question
Domains and Asymptotes
Determine the domain of each function in Exercises 69–72. Then use various limits to find the asymptotes.
y = 4 + 3x² / (x² + 1)
147views - Textbook Question
Analyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.
lim x→π/2^+ tan x
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