Download OU B.Sc 2017 Dec 1st Semester 7006 Mathematics Differential Calculus Question Paper

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Code No. 7006 / E

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FACULTY OF SCIENCE

B.Sc. I-Semester (CBCS) Examination, December 2017

Subject: Mathematics

Paper - I

Differential Calculus

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Max.Marks: 80

PART - A (5x4 = 20 Marks)

[Short Answer Type]

Note: Answer ALL the questions.

1. Find the radius of curvature of the curve y² = 2x at the point P(1,1).

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2. If w= x² + yz, x=r-s and y= r+s, then evaluate ?w/?r and ?w/?s.
3. If z = f(x+ay) + g(x-ay), then show that ?²z/?y² = a² ?²z/?x².

PART - B (4x15 = 60 Marks)

[Essay Answer Type]

Note: Answer ALL the questions.

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1. If y = (x² + x) log(x), then show that x²y_n+2 + (2n+1) xy_n+1 + n²y_n = 0

   OR

   i) State and prove Rolle’s mean value theorem.
   ii) If Rolle’s mean value theorem holds for the function f(x) = x³+ax²+bx, 1=x=2 at the point x = 4/3 then find the values of a and b.
2. Find the asymptotes of the curve x³ —6x²y+ 11xy² —6y³ +x+y+1=0.

   OR

   Find the maximum value of x + y + z, subject to the condition 1/x + 1/y + 1/z =1.

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