bca1030 smu bca Winter 2014 Ist sem assignment

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Winter 2014  ASSIGNMENT

PROGRAM-BSC IT

SEMESTER- I

SUBJECT CODE &NAME-BC1030-MATHEMATICS FOR IT

CREDIT-4

BK ID-B0947

MAX. MARKS-60

Q1.

(i) Express 792⁰ in radians and (7 π /12)⁰ in degrees

(ii) Prove that

(ii) Prove that (tanq + secq – 1)/(tanq - secq + 1) = cosq/(1- sinq ) = (1+ sinq)/ cosq

Solution:

(i)

Q2.

i. y= x^m/n being integers, n > 0 find dx/dy

ii. Differentiate log (2x + 3) from first principles

Solution.

Let y = log (2x + 3)

Let D x be a small increment in x and D y the corresponding increment in y.

Q3. Evaluate 2cosx + 3sinx/ 4 cos x + 5 sin x  dx = I

Q4  Solve dy/dx = y+x-2/ y-x-4

Solution:

The given equation is:

Q5. i. If a = cos q + i sin q,0 <q < 2p prove that 1+a/1-a = I cot q/2

ii. If x+iy= √a+ib/c+id prove that (x^2+y^2) = a^2+b^2/ c^2+d^2

Solution.

Q6 Solve: 2x + 3y + 4z = 20, x + y + 2z = 9, 3x + 2y + z = 10

Solution:

In this question,

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