Unit 1 Progress Check: MCQ Part B Final Exam (Updated 2025) 1-100 Complete Questions & Answers (Solved) 100% Correct

Unit 1 Progress Check: MCQ Part B Final Exam (Updated 2025) 1-100 Complete Questions & Answers (Solved) 100% Correct 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 4x64x6. 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 4x64x6, 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 0x50x5, 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 ? D 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 ? D 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 x3x3 and part of a parabola for x3x3. 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 ? C 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)lim⁡x→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 ? C. h(x)=⎧⎩⎨⎪⎪−8sin(π2x)8−8cos(πx)forx3forx=3forx3 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 4x64x6. 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 4x64x6, 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 0x50x5, what is limx→2f(x)limx→2f(x) ? B. 4