-1y(x+y)Q2/ Answer the following:(a) Is Rolle's Theorem applies for the function f (x) = cos(sinx) on the closedinterval [-1,1]? If it can be applied, then find the value(s) of the constant(s)...

Extracted text: Q1/ Answer the following: (a) Show that sin-1x+ cos-1x = x(x-y) (b) Find the value of tan-1 tan- where > -1 y(x+y) Q2/ Answer the following: (a) Is Rolle's Theorem applies for the function f (x) = cos(sinx) on the closed interval [-1,1]? If it can be applied, then find the value(s) of the constant(s) c. (b) Let f(x) = sin (cos-1 (sin(cos-1Vx ))). By using chain rule, show that f'(1) = Q3/ Answer the following: (a) Express sin(2 cosx) in an algebraic form. Furthermore, sketch this function and find its domain and range. csc2 (2cot-1Vx) (b) Show that J x-1 dx = 2 Vx + c. Vx+x Vx Q4/ Answer the following: (a) Simplify the function y = |x – 1| + |x + 1|. Moreover, compute the definite integral L(1x - 1| + |x + 1|) dx. Is this function differentiable at x = -1? Explain that. (*) (i) Find 3x2+x+1 sin-)+sec-1(x) d (b) (i) Compute lim cot-1 3x2-7 dx tan-1x+tan-1 x+00 Q5/ Answer the following: (a) Compute the following limits: x3+x2 +x+1 sec-1(V2+h)-sec-1/2 (i) lim x-1 (ii) lim h-0 x2-1 h cos x + 2 (b) Test the continuity of the function f (x) = x-2 at the point x = 2. x = 2