Podcast
Questions and Answers
What is the simplest form of the expression $3(x^2 y)y^{-2} z^5$?
What is the simplest form of the expression $3(x^2 y)y^{-2} z^5$?
- $3y z^5$
- $3x^2 y^3 z^5$
- $3x^2 z^5$ (correct)
- $3x^2 y z^5$
When rewriting $ln((z^{-5})^4)$ using properties of logarithms, which expression is correct?
When rewriting $ln((z^{-5})^4)$ using properties of logarithms, which expression is correct?
- $-20ln(z)$ (correct)
- $4ln(z^{-5})$
- $-4ln(z) + 4ln(5)$
- $-20ln(z) + 4ln(5)$
What is the average velocity of the baseball between $t = 0$ and $t = 2$ using the formula $s(t) = -16t^2 + 60t + 4$?
What is the average velocity of the baseball between $t = 0$ and $t = 2$ using the formula $s(t) = -16t^2 + 60t + 4$?
- $30$ feet/second
- $24$ feet/second (correct)
- $50$ feet/second
- $44$ feet/second
If the instantaneous velocity of the baseball at $t = 1$ is approximated by narrowing intervals, which average velocity interval yields the best estimate?
If the instantaneous velocity of the baseball at $t = 1$ is approximated by narrowing intervals, which average velocity interval yields the best estimate?
What is the limit of the function $f(x)$ as $x$ approaches 1?
What is the limit of the function $f(x)$ as $x$ approaches 1?
What can be inferred about the continuity of the piecewise function $f(x)$?
What can be inferred about the continuity of the piecewise function $f(x)$?
What is the result of simplifying the expression $(81^{1/2})(21^{1/2})$?
What is the result of simplifying the expression $(81^{1/2})(21^{1/2})$?
What is the expression for $ln(5e^3)$ using properties of logarithms?
What is the expression for $ln(5e^3)$ using properties of logarithms?
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Study Notes
Homework Instructions
- Complete problems on a separate sheet and upload as PDF to Canvas by September 4 at 10:10 AM.
- Bring a physical copy to class on the due date.
- Show all work and write legibly.
Question 1: Exponent Simplification
- Simplify expressions involving exponents; no negative exponents in the final answer.
- Example expressions to simplify include:
- (x²y)y⁻²z⁵ = z³
- (7b⁴)³a⁻²
- (81^(1/2))(2^(1/2))
Question 2: Logarithm Properties
- Use properties of logarithms to rewrite expressions as sums, differences, or products of logarithms.
- Expressions to rewrite include:
- ln((z⁻⁵)⁴)
- ln(5e³), where e is the irrational number.
Question 3: Motion Model of a Baseball
- The position function s(t) = -16t² + 60t + 4 describes the baseball's motion.
- Average velocity calculation:
- Find average velocity between t = 0 and t = 2.
- Understand graphical representation of average velocity.
- Instantaneous velocity estimate at t = 1:
- Calculate average velocity over three narrowing time intervals around t = 1.
- Clearly state chosen intervals and show calculation steps.
- Optional quicker method for finding instantaneous velocity is encouraged.
Question 4: Piecewise-Defined Function Analysis
- Evaluate the function f at specific points:
- Find f(1).
- Calculate lim as x approaches 1.
- Discuss the existence and value of the limit as x approaches -1; provide reasoning if it does not exist.
- Find f(3).
- Analyze continuity of function f and identify intervals of continuity.
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