Subject: Mathematics I Class: First class Dr. Ali T. Shaheen PART-I Note: Answer two questions only. All questions carry egual marks. Q.L.A) Consider the curve given by the equation ry + 3xy = 4 a) Find dy/dx using the implicit differentiation. b) Find an equation of the tangent line to the above curve at the point (1, 1). B) Derive the following function using the definition of derivative and then compute the f(x) = ! Q.2. A) Consider a function fx) which satisfies all the conditions below. derivative at (x = 4). fix) has two vertical asymptotes at x = -6 and x= -3 fix) has a horizontal asymptote at y=2 lim f(x) + lim f(x) lim f(x) = -00 -6* f12) = -2 lim f(x) = 4 lim f(x) = 1 lim f(x) = -2 f(4) = 3 i) Sketch one possible graph of the function fix). ( there are different possible graphs) ii) Determine the points at which the above function is non-continuous and give the type and the reason of discontinuity. B) For the following function, find all the asymptotes and then plot the function. -8 A(x) =- (x+ 5)(x 9) Q.3. Solve the following equations showing each step in your answer A) log: (:) + 2log,vVE + 6 = 3 B) -2(6)2x-5 + 3 = -35 C) cos(3x 10) = -0.4 Solve the equation for all values of x where Osx < 180 1 Add file