CSAT Suneung · CSAT Mathematics

Limits and differentiation

17 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 17 questions

  1. Evaluate the limit of (x^2 - 4)/(x - 2) as x approaches 2.
  2. Evaluate the limit of (x^2 - 9)/(x - 3) as x approaches 3.
  3. Evaluate the limit of (x^2 - 16)/(x - 4) as x approaches 4.
  4. Evaluate the limit of (x^2 - 25)/(x - 5) as x approaches 5.
  5. Let f(x) = 2x^3 + 3x^2 + 4x. What is f'(2)?
  6. Let f(x) = 3x^3 - 6x^2 + 2x. What is f'(2)?
  7. Let f(x) = 1x^3 + 4x^2 + 5x. What is f'(1)?
  8. Let f(x) = 4x^3 + 2x^2 + 3x. What is f'(1)?
  9. Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 4 at the point where x = 2.
  10. Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 1 at the point where x = 3.
  11. Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 5 at the point where x = 2.
  12. Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 2 at the point where x = 3.
  13. Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 1 at the point where x = 4.
  14. The function f(x) = x^3 - 12x has a local minimum at x equal to
  15. The function f(x) = -x^2 + 6x + 1 has its maximum value at x = 3. What is the maximum value?
  16. A particle moves along a line so that its position at time t is x(t) = t^3 - 6t^2 + 9t. At what value of t (t greater than 0) is it first at rest?
  17. A rectangular garden has a perimeter of 40 m. What is the largest possible area?

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