Mathematics Limits Chapter Test

Instructions and Test Details

• A 75-minute chapter test on Limits is scheduled for Friday, July 15th.
• The test includes 30 questions, combining multiple-choice and numerical questions.
• Time allocation for the test is 75 minutes.
• Total marks for the exam are 100.

Marking Scheme

• Mathematics Single Correct:
  • 4 marks for a correct answer.
  • -1 mark for an incorrect answer.
  • 0 marks for no response.
• Mathematics Numerical:
  • Maximum attempts in this section are 5 questions.
  • 4 marks for a correct answer.
  • -1 mark for an incorrect answer.
  • 0 marks for no response.

Example Questions (Mathematics Single Correct)

• Question 1: Find lim_x→0 (tan¹²x)/x². Possible answers are 0, 1, 3, ∞
• Question 2: Evaluate lim_x→0 [(2×tan2x - 2xtanx)/(1-cos2x)²]. Possible answers are -2, 1/2, 1, 2.
• Question 3: Determine lim_x→∞(√x + √x + √x - √x). Possible answers are 0, 1, log₂, none of these.
• Question 4: Calculate lim_x→0 [(|3x + 4|² - (2 - √x)²)/x]. Possible answers are 5, 2, 0, 10.
• Question 5: If lim_x→∞ f(x) exists and is finite and lim_x→∞ (3f(x) -1)/(f(x) + 3f(x)) = 3, find the value of lim_x→∞ f(x). Possible answers are 1, -1, 2, none of these.
• Question 6: Evaluate lim_x→∞ [(x³ - x)/(√(1 + x⁶))]. Possible answers are -1, 0, 1, 3.
• Question 7: Determine lim_x→0 [log(1 + 2x) + 1]/x^2. Possible answers are 1/2, 2, 1, none of these.
• Question 8: Calculate lim_x→0 [sin(cos²x)] /x². Possible answers are π, π/2, 1.
• Question 9: Evaluate lim_x→2 [(cos²x + sin²x - 1)/(x - 2)]. Possible answers are 0, non existence and more.
• **Question 10:**Find the value of lim_x→0 [(sin^-1(1 / x))/(2x)]^{1/(1 + x2}. Possibile answers are 1, 2, does not exist, more.
• Question 11: Evaluate lim_x→0[√(1 - cos2x)]/x. Possible answers are -1, 0, 1 and more

Example Questions (Mathematics Numerical)

• Question 1: Given f(x) is a polynomial. If f(x)f(1/x) = f(x) + f(1/x), and f(2) > 1, find lim_x→1 f(x).
• Question 2: Find lim_x→1-[ sin^-1(2x - 1)/(x - 1)].
• Question 3: Determine lim_n→∞ [(1²/n²) + (2²/n²) +....(n²/n²)].
• Question 4: If lim_x→∞ [(√(ax² - x + 1)) / (ax)] = 0, what is the value of 'a' and 'b'?
• Question 5: Let f : R → R⁺ be a positive increasing function with lim_x→∞ f(x)/f(3x) / f(2x)/f(x) = 1. Find lim_x→∞ f(x). This is important and will be on the exam
• Question 6: Find all values of a such that lim_x→a [(x⁹ - a⁹)/(x - 9)] = lim_x→3 [6 + x]

This is a 75-minute chapter test on Limits in Mathematics, scheduled for July 15th. It consists of 30 questions, including multiple-choice and numerical problems, with a total of 100 marks available. Be prepared to apply your knowledge of limits and evaluate expressions accurately.