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Thursday, January 7, 2016

CALCULUS : Question Paper First Semester B.tech Degree Examination, January 2016 (Free Download)


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FIRST SEMESTER B.TECH DEGREE EXAMINATION, JANUARY 2016

Course Code: MA101

Course Name: CALCULUS

Max. Marks: 100                                                       Duration: 3 Hours 

PART A 



Answer all questions, each question carries 3 marks

  1. Show that the series  is convergent. 
  2. Find   
  3. Identify the surfaces .
  4. Equation of a surface in spherical coordinates is  Find the equation of this surface in rectangular coordinates.
  5. Given show that the function satisfies the Laplace equation .
  6.  Let where  Find  using chain rule.
  7.  particle moves along a circular helix in 3-space so that its position vector at time t is r(t). (4 cos r t)i + (4 sin r t)j + tk Find the displacement of the particle during the interval .
  8. Find the tangent to the curve r(t) = at t = 1.
  9. Evaluate .
  10. The line y = 2 - x and the parabola intersect at the points (-2, 4) and (1, 1),If R is the region enclosed by y=2-x and ,then find .
 (10 x 3 = 30 Marks)

PART-B 


Answer any 2 complete questions each having 7 marks

  1. Find the radius of convergence and interval of convergence of the series .
  2. Test the convergence of  
  3. Find the Taylors series of  about x = 1. 
  4.  
     Answer any 2 complete questions each having 7 marks
     
  1. Find the domains of   (ii)  and describe them in words.
  2. Find the limit of   as along (i) the X-axis , (ii) the Y- axis (iii) the line y = x.
  3. Find the spherical and cylindrical coordinates of the point that has rectangular coordinates

Answer any 2 complete questions each having 7 marks

  1. Locate all relative maxima , relative minima and saddle point if any,of  .
  2. Let f be a differentiable function of 3 variables and suppose that   prove that .
  3. Find the local linear approximation L(x,y) to f(x,y) = at the point P(4,3). Compare the error in approximating 'f' by L at the specified point Q (3.92, 3.01) with the distance between P and Q.

Answer any 2 complete questions each having 7 marks

  1. Find y(t) where   .
  2. Find the arc length parametrization of the line x = 1 + t,y = 3 - 2t, z = 4 + 2t that has the same direction as the given line and has reference point (1, 3, 4).
  3. Find the directional derivative of at    in the direction of PQ where Q is the origin.

Answer any 2 complete questions each having 7 marks

  1. Find the area bounded by the x-axis, Y = 2x and x+y=1 using double integration.
  2. Use a triple integral to find the volume of the solid ,within the cylinder  and between the planes z = 1 and x + z = 5.
  3. Sketch the region of integration and evaluate the integral  by changing the order y of integration.

Don't Forget to mail any type of study material to eduktu@gmail.com.
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