Math Problem Statement

Quiz 1 (1.1-1.3).pdf

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Solution

The document you've uploaded is a quiz for a Calculus I course (MATH 1950) covering topics from sections 1.1 to 1.3. Here are the problems listed in the quiz:

  1. Limits from a Graph: You are asked to determine several limits based on a graph of a function f(x)f(x). If the limit does not exist, you should write "DNE".

  2. Calculating Limits: Problems 7 through 10 ask you to calculate limits without using L'Hôpital's rule.

  3. Evaluating a Piecewise Function: Problem 11 requires evaluating the limit of a piecewise function as xx approaches a specific value.

  4. Continuity: Problem 13 asks you to determine if a function is continuous on a given interval and, if not, whether the discontinuity is removable or non-removable.

  5. Intermediate Value Theorem: Problem 14 involves using the Intermediate Value Theorem to verify that a function has a zero within a specific interval.

Would you like detailed solutions for these problems or explanations on specific questions?

Here are five related questions to consider:

  1. What are the conditions for a limit to exist at a particular point?
  2. How do you determine if a function is continuous at a point?
  3. When is L'Hôpital's rule applicable for solving limits?
  4. What is the significance of the Intermediate Value Theorem in calculus?
  5. How do you identify removable and non-removable discontinuities?

Tip: When solving limit problems graphically, make sure to check the left-hand limit, right-hand limit, and the function's value at the point for consistency.

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Math Problem Analysis

Mathematical Concepts

Limits
Continuity
Piecewise Functions
Intermediate Value Theorem

Formulas

Limit definition
Continuity conditions

Theorems

Intermediate Value Theorem

Suitable Grade Level

Undergraduate Calculus I