Mathematics II — CAMT154 (2nd Sem)

wi i Tribhuvan University f x OK Faculty of Humanities & Social Sciences {fie aphima PS OFFICE OF THE DEAN wy 2021 Bachelor in Computer Applications Full Marks: 60 Course Title: Mathematics II Pass Marks: 24 Code No: CAMT154 Time: 3 hours Semester: II Candidates are required to answer the questions in their own words as far as possible. Group B Attempt any SIX questions. [6x5 = 39] Q. A function Kix) is defined as 2x +3 for —3/2<x<0 Kx)=43-2x for0<x<3/2 —3-2x for x>3/2 Show that f(x) is continuous at x = 0 and discontinuous at x = 3/2. 6) Find the a when x = a(t + sin A), y= a(1—cos f) . 5 limit xe* —Ind+x 4. State L 'Hospitl's Rule. Use it to evaluate: ne eset 2) x—>0 x e State Roll's Theorem. Verify the Rolle's Theorem for the function fx) = x*— 9 in the interval —3 <x $3. 2 dx, 2x +5 Evaluate: a) | ——— b) | ———a« © ) J LoS \aas 7. Solve: sin x2 +(cosx)y=-—sinx cosx (® Solve the following system of equations by Gauss-Seidel method —4x+y—z=-8 Bx Oye 22 | LV 232-2 Group C Attempt any TWO questions. [2x10 = 20] 9. Using simplex method, find the optima! solution of Z = 7x1 + 5x2 subject to x1 + 2x2<6 4x1 + 3x2 <6 Xp > Oe. 0 10. What do you mean by stationary points and inflection points? Using derivatives, find two numbers whose sum is 20 and sum of whose squares is minimum. . 1 ‘i 11. Using Simpson's ; rule, evaluate, ds with 3 points of intervals. Find the error of x : 0 approximation. How many points are to be considered to make the approximation value within 10°?