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.
- 4×Asked in 2026, 2024, 2023, 2022Evaluate the limit, x ( x xx )Answer coming5
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- Evaluate the limit, x ( x xx )TU Board 2026
- Evaluate x 4 x xx 4TU Board 2024
- Evaluate the limit x x xx .TU Board 2023
- Solve: x dydx + ( x) y = x x .TU Board 2022
- 3×Asked in 2026, 2024, 2022A 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
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- 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 ?TU Board 2026
- A function f(x) is defined as f(x) = cases 2x + 3 & for x < 1 \\ 4 & for x = 1 \\ 6x 1 & for x 1 cases Is the function f(x) continuous at x = 1 ? If not, how can you make it continuous at x = 1 ?TU Board 2024
- "A function f(x) is defined as f(x) = cases 2x + 3 & for 32 x < 0 \\ 3 2x & for 0 x 32 \\ 3 2x & for x 32 cases show that f(x) is continuous at x = 0 and discontinuous at x = 32 ."TU Board 2022
- 2×Asked in 2024, 2023Compute 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
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- 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…TU Board 2024
- Compute the approximate value of the integrate 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…TU Board 2023
- 2×Asked in 2023, 2022Evaluate the integral a. 2x + 5 x^2 + 5x\,dx b. e^2x\, x\,dxAnswer coming5
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- 2×Asked in 2026, 2023Evaluate 0^2 1+x^3\,dx by using Simpson's 13 rule by taking n=4 .Answer coming5
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- 2×Asked in 2026, 2022Find dydx if (a) x=t^2 1,\ y=t^4 1 (b) x^2+y^2= xyAnswer coming5
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- Find dydx if (a) x=t^2 1,\ y=t^4 1 (b) x^2+y^2= xyTU Board 2026
- Find dydx when x = a(t + t) , y = a(1 t) .TU Board 2022
- 2×Asked in 2026, 2023Find the maximum and minimum values of the function f(x)=4x^3 15x^2+12x 1 . Also, find the point of inflection.Answer coming5
- 2×Asked in 2026, 2024Find the derivative of the function f(x)= 1 x by using first principle.Answer coming5
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- 2×Asked in 2026, 2023Solve the differential equations 2 dydx=2 yx+ y^2x^2Answer coming5
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- 2×Asked in 2024, 2022State 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
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- 2×Asked in 2026, 2023State 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
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- 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…TU Board 2026
- Verify Rolle's theorem for the function f(x) = x,\;x [0, ] and find the point on the curve where the tangent is parallel to the x axis.TU Board 2023