MT1710: Calculus 16 January 2019 Test - you have 45 minutes to complete the test Before you start: Have you writen down your candidate number on the front page of your script book? * Is your name and student number written on the right side, which is folded so that is not visible to the marker? Questions 1. Consider the the quartic expression f(x)=x4+ x3 + x2 - 1, (a) Use Descartes Rule of Signs to determine the possible number of zeros of f(x). (12 Marks) (b) Hence, using the Intermediate value Theorem, prove that f(x) has just two real zeros and find them; if there is a non-integer zero, it is sufficient to locate the consec- utive integers between which that zero lies. 2. Find the real solution(s) of the equation (16 Marks) cosh x = 2(1 + e2) . 3. Evaluate dt V5 + 4t - t2 (20 Marks) . 4. Solve the differential equation dx (1+22)49 - xy= 2x(1+ 22)2 , subject to y(0) = 1. 5. Find the general solution of the differential equation ?2y dx2 - 4 dy dx + 4y = 4x ea . (12 Marks) (20 Marks) (20 Marks) F. Mota-Furtado