Podcast Beta
Questions and Answers
Simplify: (a) ln(e^10) (b) e^5 (c) ln(10)
a. 10, b. e^5, c. ln(10)
Evaluate the limit: (a) lim(sqrt(x^2 - 9), x->5) (b) lim((x^2 -3x + 2)/(x^2 - 4), x->2)
a. 4, b. 1
Find f'(x) for: (a) f(x) = (1-2x)(x-x^2) (b) f(x) = (2x^3 + cos(x) + 7)^30
a. -3x^2 + 5x - 2, b. 30(2x^3 + cos(x) + 7)^29(6x^2 - sin(x))
For a function, find the average rate of change over [-3.0, 2.2]. State if the function is increasing or decreasing.
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If $1000 is invested at 5.5%, calculate the amount after 8 years for: (a) Annually (b) Quarterly (c) Monthly (d) Daily (e) Continuously
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Given r = 3 + 3 cos(theta), state the name of the classical curve, provide information for graphing, and graph the curve.
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Study Notes
Math 4R Final Review
- The final review consists of 32 questions, covering various topics in mathematics.
- The topics include limits, derivatives, graphing, exponential equations, and more.
Limits
- Evaluate the given limits, such as:
- lim (x^3 + 3x^2 - 2x - 17) as x approaches 1
- lim (x^2 - 1) / (3x^2 - 2x - 15) as x approaches -1
- lim (x^2 - 3x - 18) / (x^2 + x - 6) as x approaches -3
Derivatives
- Find the derivative of each function, such as:
- f(x) = (1 - 2x)(x - x^2)
- f(x) = (2x^3 + cos(x) + 7) / 30
- f(x) = (1 - 2x^2) / (3x^3)
Graphing
- Do a complete analysis and graph the given function, such as:
- f(x) = 2x - 6 / (x^2 - 3x)
- f(x) = 2x^3 - 2x^2 / (x - 9x)
Exponential Equations
- Solve the exponential equations, such as:
- 3 + 8.5x = 2
- 7.5x + 2 = 23
Other Topics
- Identify each function as even, odd, or neither, such as:
- f(x) = x^2 - 4x + 3
- f(x) = x^4 - 5x^2 + 4
- f(x) = x^3 - 7x^2 + 14x - 7
- Solve the equations for all values in the interval from 0 ≤ x ≤ 2π, such as:
- 2 cos(x) + √3 = 0
- 3 tan(x) - √3 = 0
- Evaluate the given limits, such as:
- lim (x^3 + 3x^2 - 2x - 17) as x approaches 1
- lim (x^2 - 1) / (3x^2 - 2x - 15) as x approaches -1
- lim (x^2 - 3x - 18) / (x^2 + x - 6) as x approaches -3
Symmetry and Graphing
- Identify the symmetry of each function, such as:
- f(x) = 2 + 5 sin(θ)
- f(x) = 3 + 3 cos(θ)
- Graph the curve, such as:
- r = 2 + 5 sin(θ)
- r = 3 + 3 cos(θ)
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Description
Review questions and practice exercises for the Math 4R final exam, covering topics from worksheets 1-32. Prepare for the exam on June 10th and 11th.
