Question

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

over[0,+∞).

Q2. Let g(x)=(x^{2}+1)^{sinx}.

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

(b) Explain why g is diﬀerentiable, and then ﬁnd the derivative of g.

Q3.Let f(x)=∣x+3∣^{3/2}/ ∣x−4∣ .

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

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