MTH117 Mathematics I
Mathematics I: 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.
- 5×Asked in 2079, 2077, 2075, 2074Prove that x 0 x x the does not exist.Answer coming10
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- Prove that x 0 x x the does not exist.TU Board 2079
- If f(x,y) = xyx^2 + y^2 , does f(x, y) exist, as (x, y) → (0, 0)?TU Board 2077
- If f(x, y) = yx does (x,y) (0, 0) f(x, y) exists? JustifyTU Board 2075
- Prove that the x 2 x – 2 x – 2 doesn't exist.TU Board 2075
- Prove that x 0 x x the does not exist.TU Board 2074
- 3×Asked in 2079, 2078, 2074Define initial value problem. Solve: y^H+y^' 6y =0, y(0)=1, y^'(0)=0Answer coming10
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- 3×Asked in 2079, 2078, 2077Find the derivative of (r(t)) = t^2i – te^( t)j + sin(2t)k and find the unit tangent vector at t = 0Answer coming5
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- Find the derivative of (r(t)) = t^2i – te^( t)j + sin(2t)k and find the unit tangent vector at t = 0TU Board 2079
- Find the derivatives of r(t) = (1 + t^2)i – te^ tj + sin 2tk and find the unit tangent vector at t=0 .TU Board 2078
- Find the derivatives of r(t) = (1 + t^2)i – te^ tj + sin 2tk and find the unit tangent vector at t=0 .TU Board 2077
- 3×Asked in 2079, 2078, 2077Find the equation of the tangent at (1,3) to the curve y=^2x^2 + 1.Answer coming5
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- 3×Asked in 2077, 2075, 2074Find the Maclaurin series for cos x and prove that it represents cos x for all x.Answer coming10
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- 3×Asked in 2079, 2078, 2077Find the partial derivative f xx and f yy of f(x,y)= x^2 + x^3y^2 – y^2 + xy, at (1,2).Answer coming5
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- 3×Asked in 2079, 2077, 2075Starting with x 1= 1, find the third approximate x 3 to the root of the equation x³ – x – 5 = 0Answer coming5
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- Starting with x 1= 1, find the third approximate x 3 to the root of the equation x³ – x – 5 = 0TU Board 2079
- Find the third approximation x 3 to the root of the equation f(x) = x^3 – 2x – 7 , setting x 1 = 2 .TU Board 2077
- Stating with x 1 = 2, find the third approximation x 3 to the root of the equation x^3 – 2x – 5 = 0TU Board 2075
- 3×Asked in 2078, 2077, 2075Find the volume of the solid obtained by rotating about the y axis the region between y = x and y = x^2.Answer coming5
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- Find the volume of the solid obtained by rotating about the y axis the region between y = x and y = x^2.TU Board 2078
- Find the volume of the solid obtained by rotating about the y axis the region between y = x and y = x^2.TU Board 2077
- Find the volume of the resulting solid which is enclosed by the curve y = x and y = x^2 is rotated about the x axis.TU Board 2075
- 3×Asked in 2079, 2077, 2074Sketch the curve y=x^2 +1 with the guidelines of sketching.Answer coming10
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- Sketch the curve y=x^2 +1 with the guidelines of sketching.TU Board 2079
- Sketch the curve y = 1x – 3TU Board 2077
- Sketch the curve y = x^3 + xTU Board 2074
- 3×Asked in 2079, 2078, 2077State Rolle's theorem and verify the theorem for f(x) = x^2 – 9, x ε[ 3,3]Answer coming5
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- 2×Asked in 2079, 2075If a function is defined by f(x)=1+x, if x<= 1 x^2, if x 1, evaluate f( 3), f( 1) and f(0) and sketch the graph.Answer coming10
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- 2×Asked in 2079, 2078A particle moves a line so that its velocity v at time t is (1) Find the displacement of the particle during the fine period 1 ≤ t ≤ 4 (2) Find the distance travelled during this time period.Answer coming10
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- A particle moves a line so that its velocity v at time t is (1) Find the displacement of the particle during the fine period 1 ≤ t ≤ 4 (2) Find the distance travelled during this time period.TU Board 2079
- A particle moves along a line so that its velocity v at time t is v = t^2 – t + 6 1. Find the displacement of the particle during the time period 1 ≤ t ≤ 4. 1. Find the distance travelled during…TU Board 2078
- 2×Asked in 2075, 2074Calculate R f(x,y) dA for f(x,y) = 100 – 6x^2y and R: 0 x 2, 1 y 1Answer coming10
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- 2×Asked in 2077, 2075Define continuity of a function at a point x = a . Show that the function f(x) = 1 x^2 is continuous on the interval[1, 1].Answer coming5
- 2×Asked in 2077, 2075Show that the series n=0^∞ 11 + n^2 converges.Answer coming5
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- 2×Asked in 2079, 2077Dry air is moving upward. If the ground temperature is 20^° and the temperature at a height of 2km is 10^° c, express the temperature T in ^° c as a function of the height h(in km), assuming that a linear model is appropriate. (b) Draw the graph of the…Answer coming5
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- Dry air is moving upward. If the ground temperature is 20^° and the temperature at a height of 2km is 10^° c, express the temperature T in ^° c as a function of the height h(in km), assuming that a…TU Board 2079
- Dry air is moving upward. If the ground temperature is 20^0 and the temperature at a height of 1km is 10^0 C, express the temperature T in ^0C as a function of the height h (in kilometers), assuming…TU Board 2077
- 2×Asked in 2075, 2074Estimate the area between the curve y = x^2 and the lines y = 1 and y = 2.Answer coming10
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- 2×Asked in 2078, 2077Find a vector perpendicular to the plane that passes through the points:p(1, 4, 6), Q( 2, 5, 1) and R(1. 1, 1)Answer coming5
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- 2×Asked in 2078, 2077Find the local maximum and minimum values, saddle points of f(x,y) = x^4 + y^4 – 4xy + 1Answer coming5
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- 2×Asked in 2075, 2074Find the solution of y" + 4y' + 4 = 0.Answer coming5
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- Find the solution of y" + 4y' + 4 = 0.TU Board 2075
- Find the solution of y"+6y'+9=0, y(0)=2, y'(0)=1TU Board 2074
- 2×Asked in 2075, 2074Find the volume of a sphere of radius rAnswer coming10
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- Find the volume of a sphere of radius rTU Board 2075
- Find the volume of a sphere of radius rTU Board 2074
- 2×Asked in 2075, 2074Verify Mean value theorem of f(x) = x^3 – 3x + 2 for [ 1, 2].Answer coming5
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- 2×Asked in 2079, 2078What is sequence? Is the sequence a n = n 5 + n convergent?Answer coming5
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