(Solved): Question 1 (4 points) Calculate the improper integral if it converges, or show that it diverges. ...

Question 1 (4 points) Calculate the improper integral if it converges, or show that it diverges. $${?}_0^1\frac{3x^4}{x^5?1}dx$$ Question 2 (4 points) The "Tribonacci" sequence is the sequence defined by $$T_0=T_1=T_2=1$$ and $$T_{n+3}=T_n+T_{n+1}+T_{n+2}$$ for $$n?0$$. (a) Is this sequence defined implicitly or explicitly? Explain your answer. (b) Write down all of the terms in the sequence that are below 500 . Question 2 (4 points) The "Tribonacci" sequence is the sequence defined by $$T_0=T_1=T_2=1$$ and $$T_{n+3}=T_n+T_{n+1}+T_{n+2}$$ for $$n?0$$. (a) Is this sequence defined implicitly or explicitly? Explain your answer. (b) Write down all of the terms in the sequence that are below 500 .