CALCULUS — DU B.Sc (hons) Statistics Previous Year Question Papers

(b) Show that I cossx dx =J sin-r + (a) Discuss thc derivability of the lunction : Your Roll N o.,..,...,....., Sr, No, of Question Paper: 1405 Name of thc Cou rsc B.Sc. (Hons) Statistics (NEP- atx=1and2 (b) By the elimination of the constants h and k, find the differential equation for which (x - h)2 + 2. Attempt six qucstions in all. l. (a) Show that the function f, defined by f(x) = (1 + 3L)tt* when x*0, f(0) = e3, is continuous for x :0. (b) If y=xlog1, prove that d.ny 2. (a) Determine rinl(4- cot'r) (b) If A, B, C are the angles of a triangle such that sin2A + sin2B + sin2C = Constant, prove that dA dB tan /4-tan B tan C-tan.4' 3 (a) Evaluate Jl xy(x + y) dx dy over the area between ff* y(x sin x * cosr) =1. (a) Solve the partial differential equation p(qr+l)+(b-z)q:0. (b) Show that I:tz ^ltane dt =ip G, i) =rti *0, 5. (a) Change the order of integration in the integral ff !E:af@,fla'aY (b) Find y"(0) when y = tog(r + ,/*7). (a) Assuming the validity of differentiation under integral sign, show that t@ --Z , 1 r- 1az Jo e ' cosaxax=;!fie 4 (b) Solve the partial differential equation, il2 z d2z ""- : COS .r COS ZY.