Explanations and answers to all questions

1. [ 1 mark ] [MC] Given the function; y = In (tan x), then: f ( x ) + 1 s dy cos x dx sinx JX " fx ( lil toomse ) ) dx dy = 2 sin(2x) b. dy dx = cotx tin x d. dx dy = 2 csc(2x) cus " ( * ) tanx . the cus? ( x ) cosx 2. [ 1 mark ] [MC] Given the function; y = x , then: e- 1 Imy #1xx a. dy dx = ex dy dx = x In x b. dy dx = x + 1 YENE d dy dx = d x = * " . fixed a 1 - 3. [ 1 mark each ] State the exact value, the value of each of the following limits: a. lim e secx b. lim 7 x-7 let X - 7 : 4 let A : sexx X -7 8 - 7 7 7:0107 : 80 X SL = 1 I O X 4. [ 2 marks ] Use Logarithmic Differentiation to find the equation line of the tangent to y = Vx+1(x- 6x+1) at any form Vx - 6 the point (7, 16) ye Jx + 1 ( x 2 - 6 x + 1 ) JX - 6