Unit 1 Progress Check: MCQ Part B
As 𝑥 → 0 x→0, the numerator stays 0 while the denominator approaches 0, causing the expression to become undefined. Therefore, the limit does not exist.
If ff is the function defined by f(x)=1x−1x−1f(x)=1x−1x−1, then limx→1f(x)limx→1f(x) is equivalent to which of the following?
A. limx→1(−1x)
Key Terms
If ff is the function defined by f(x)=1x−1x−1f(x)=1x−1x−1, then limx→1f(x)limx→1f(x) is equivalent to which of the following?
A. limx→1(−1x)
Let ff and gg be functions such that limx→4g(x)=2limx→4g(x)=2 and limx→4f(x)g(x)=πlimx→4f(x)g(x)=π. What is limx→4f(x)limx→4f(x) ?
C. 2π
If ff is the function defined above, then limx→0f(x)limx→0f(x) is
D. nonexistent
The function ff is defined for all xx in the interval 4<x<64<x<6. Which of the following statements, if true, implies that limx→5f(x)=17limx→5f(x)=17 ?
D. There exist functions gg and hh with g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 4<x<64<x<6, and limx→5g(x)=limx→5h(x)=17limx→5g(x)=limx→5h(x)=...
The function gg is given by g(x)=7x−26x−5g(x)=7x−26x−5. The function hh is given by h(x)=3x+142x+1h(x)=3x+142x+1. If ff is a function that satisfies g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 0<x<50<x<5, what is limx→2f(x)limx→2f(x) ?
B. 4
Let ff be a function of xx. The value of limx→af(x)limx→af(x) can be found using the squeeze theorem with the functions gg and hh. Which of the following could be graphs of ff, gg, and hh ?
Related Flashcard Decks
Study Tips
- Press F to enter focus mode for distraction-free studying
- Review cards regularly to improve retention
- Try to recall the answer before flipping the card
- Share this deck with friends to study together
| Term | Definition |
|---|---|
If ff is the function defined by f(x)=1x−1x−1f(x)=1x−1x−1, then limx→1f(x)limx→1f(x) is equivalent to which of the following? | A. limx→1(−1x) |
Let ff and gg be functions such that limx→4g(x)=2limx→4g(x)=2 and limx→4f(x)g(x)=πlimx→4f(x)g(x)=π. What is limx→4f(x)limx→4f(x) ? | C. 2π |
If ff is the function defined above, then limx→0f(x)limx→0f(x) is | D. nonexistent |
The function ff is defined for all xx in the interval 4<x<64<x<6. Which of the following statements, if true, implies that limx→5f(x)=17limx→5f(x)=17 ? | D. There exist functions gg and hh with g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 4<x<64<x<6, and limx→5g(x)=limx→5h(x)=17limx→5g(x)=limx→5h(x)=17. |
The function gg is given by g(x)=7x−26x−5g(x)=7x−26x−5. The function hh is given by h(x)=3x+142x+1h(x)=3x+142x+1. If ff is a function that satisfies g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 0<x<50<x<5, what is limx→2f(x)limx→2f(x) ? | B. 4 |
Let ff be a function of xx. The value of limx→af(x)limx→af(x) can be found using the squeeze theorem with the functions gg and hh. Which of the following could be graphs of ff, gg, and hh ? | |
The table above gives selected values for a function ff. Based on the data in the table, which of the following could not be the graph of ff on the interval 1.9≤x≤2.11.9≤x≤2.1 ? | The correct graph must match the table’s values, so any graph that does not pass through or align with those points on the interval 1.9≤x≤2.11.9 \leq x \leq 2.11.9≤x≤2.1 could not be the graph of fff. |
Let ff be the piecewise function defined above. Also shown is a portion of the graph of ff. What is the value of limx→2f(f(x))limx→2f(f(x)) ? | D. 1/2 |
The table above gives selected values for a function ff. Also shown is a portion of the graph of ff. The graph consists of a line segment for x<3x<3 and part of a parabola for x>3x>3. What is limx→3f(x)limx→3f(x) ? | A. 1.6 |
The function ff is defined above. Which of the following statements is true? | B. ff has a removable discontinuity at x=2x=2 |
The function ff has a jump discontinuity at x=3x=3. Which of the following could be the graph of ff ? | A jump discontinuity at x=3x = 3x=3 means the function "jumps" from one value to another at that point. |
The graph of a function ff is shown in the figure above. At what value of xx does ff have a removable discontinuity? | B. x=3 |
If limx→6f(x)limx→6f(x) exists with limx→6f(x)<5limx→6f(x)<5 and f(6)=10f(6)=10, which of the following statements must be false? | D. ff is continuous at x=6x=6. |
Let f be the function defined above. Which of the following statements is true? | B. ff is not continuous at x=1x=1 because f(1)f(1) does not exist. |
Which of the following functions is continuous at x=3 ? |