Higher Secondary Certificate Examination (Bangladesh) · Higher Mathematics

Calculus - Limits, Differential and Integral Calculus

35 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 35 questions

  1. What is the limit of (sin x) / x as x approaches 0?
  2. What is the derivative of f(x) = x^5 - 4x^3 + 7x - 9 with respect to x?
  3. What is the derivative of f(x) = sin(3x) with respect to x?
  4. What is the derivative of f(x) = ln(x) with respect to x for x > 0?
  5. What is the derivative of f(x) = e^(2x) with respect to x?
  6. What is the slope of the tangent line to the curve y = x^2 - 3x + 2 at x = 4?
  7. At which value of x does the function f(x) = x^2 - 6x + 5 have a local minimum?
  8. What is the indefinite integral of (3x^2 + 4x - 5) dx?
  9. What is the definite integral of 2x dx from x = 1 to x = 3?
  10. What is the limit of (x^2 - 9) / (x - 3) as x approaches 3?
  11. What is the derivative of y = tan(x) with respect to x?
  12. What is the derivative of y = ln(sin x) with respect to x?
  13. What is the integral of (1 / x) dx for x > 0?
  14. What is the derivative of y = u * v by the Product Rule?
  15. What is the limit of (1 - cos x) / x^2 as x approaches 0?
  16. What is the definite integral of cos(x) dx from 0 to pi/2?
  17. What is the derivative of y = arcsin(x) with respect to x?
  18. What is the derivative of y = arctan(x) with respect to x?
  19. If y = x^x, what is dy/dx for x > 0? (Hard)
  20. What is the integral of e^(3x) dx?
  21. What is the area of the region bounded by y = x^2, the x-axis, and the lines x = 0 and x = 3?
  22. What is the slope of the normal to the curve y = x^3 at x = 1?
  23. What is the second derivative d^2y/dx^2 of y = sin(x)?
  24. What is the value of limit as x approaches infinity of (3x^2 + 5x) / (2x^2 - 7)?
  25. At a point of inflection of y = f(x), what is the value of d^2y/dx^2?
  26. What is the value of the definite integral of x^3 dx from x = -2 to x = 2?
  27. What is the derivative of y = sec(x) with respect to x?
  28. What is the integral of tan(x) dx?
  29. What is the limit of (e^x - 1) / x as x approaches 0?
  30. What is the integral of 1 / (1 + x^2) dx?
  31. By Integration by Parts, what is the formula for integral of u (dv/dx) dx?
  32. What is the maximum value of f(x) = sin(x) + cos(x)? (Hard)
  33. What is the derivative of y = ln(x^2 + 1) with respect to x?
  34. What is the definite integral of 1/x dx from 1 to e?
  35. What is the derivative of y = a^x with respect to x (a > 0, a != 1)?

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