Q1. Let f(x)=x(1+sin(/x)), x>0. Determine whether it is possible to extend f to a continuous function f over[0,+).

Q2. Let g(x)=(x²+1)^sinx.

(a) Without using dierentiability of g, explain why g is continuous.

(b) Explain why g is dierentiable, and then nd the derivative of g.

Q3.Let f(x)=x+3^3/2/ x4 .

(a) Write f as a case-dened function.

(b) Compute the derivative of f. You should determine when you can use the formulas of derivatives and rules of dierentiation and when you should apply the denition of derivative.