CAMT154 Mathematics II

Mathematics II: most repeated questions

Questions that have come up in more than one paper, matched by what they ask rather than exact wording. Most repeated first.

  1. 4×Asked in 2026, 2024, 2023, 2022
    Evaluate the limit, x ( x xx )Answer coming5
    See the wording in each paper
  2. 3×Asked in 2026, 2024, 2022
    A function f(x) is defined as f(x)=2x+3 for x<1 f(x)=4 for x=1 f(x)=6x 1 for x 1 Is the function f(x) is continuous at x=1 ? If not, how can you make it continuous at x=1 ?Answer coming5
    See the wording in each paper
  3. 2×Asked in 2024, 2023
    Compute the approximate value of the integral 11 + x^2\,dx by using the composite trapezoidal rule with three points, and compare the result with the actual value. Determine the error formula and numerically verify an upper bound on it.Answer coming10
    See the wording in each paper
  4. 2×Asked in 2023, 2022
    Evaluate the integral a. 2x + 5 x^2 + 5x\,dx b. e^2x\, x\,dxAnswer coming5
    See the wording in each paper
  5. 2×Asked in 2026, 2023
    Evaluate 0^2 1+x^3\,dx by using Simpson's 13 rule by taking n=4 .Answer coming5
    See the wording in each paper
  6. 2×Asked in 2026, 2022
    Find dydx if (a) x=t^2 1,\ y=t^4 1 (b) x^2+y^2= xyAnswer coming5
    See the wording in each paper
  7. 2×Asked in 2026, 2023
    Find the maximum and minimum values of the function f(x)=4x^3 15x^2+12x 1 . Also, find the point of inflection.Answer coming5
    See the wording in each paper
  8. 2×Asked in 2026, 2024
    Find the derivative of the function f(x)= 1 x by using first principle.Answer coming5
    See the wording in each paper
  9. 2×Asked in 2026, 2023
    Solve the differential equations 2 dydx=2 yx+ y^2x^2Answer coming5
    See the wording in each paper
  10. 2×Asked in 2024, 2022
    State Mean Value Theorem. Give its geometrical meaning. Verify the Mean Value Theorem for the function f(x) = x^3 + x^2 6x in the interval [ 1, 4] .Answer coming5
    See the wording in each paper
  11. 2×Asked in 2026, 2023
    State Rolle's theorem and Lagrange's mean value theorem with their geometrical interpretation. Verify Rolle's theorem for the function f(x)= x,\ x [0, ] . Also find a point on the curve represented by given function where the target is parallel to x axis.Answer coming10
    See the wording in each paper