Topic 1: Functions and Their Properties
1\( x \neq 2 \)
2Even
3\( 5 \)
4\( [1, \infty) \)
5No
6\( f^{-1}(x) = \frac{x - 3}{2} \)
7Domain: \( x \geq 1 \), Range: \( y \geq 0 \)
8Even
9\( (x + 1)^2 \)
10\( f^{-1}(x) = \frac{x + 1}{x - 2} \), Domain: \( x \neq 2 \)
11Yes
Topic 2: Limits and Their Intuitive Meaning
1\( 4 \)
2Does not exist
3\( 2 \)
4\( 7 \)
5\( 1 \)
6Does not exist (oscillatory)
7\( 2 \)
8\( 0.5 \)
9\( -\infty \)
10\( 1 \)
Topic 3: Limit Laws and Evaluation Techniques
1\( 5 \)
2\( 5 \)
3\( 2 \)
4\( 0 \)
5\( 2 \)
6\( 2 \)
7\( 1 \)
8\( 0 \)
9\( \frac{1}{2} \)
10\( 0 \)
Topic 4: Continuity and Types of Discontinuities
1Yes
2No (infinite discontinuity)
3Removable
4Yes
5Oscillatory
6Removable (limit is 2)
7Yes, except at \( x = 1 \) (removable)
8Infinite at \( x = 0 \), removable elsewhere
Topic 5: Introduction to the Concept of a Derivative
1\( 2x \)
2\( 3 \)
3\( 12 \)
4\( \frac{1}{2\sqrt{x}} \)
5\( -\frac{1}{x^2} \)
6\( 1 \)
7\( \cos x \)
8\( -\frac{2}{x^3} \)