Problem $2(10$ points each$)$

Suppose an algorithm solves a problem of input size $n$ in at most the number of steps listed for each $T(n)$ given below. Calculate the Big$-($not just Big$-$O$)$ for each $T(n).$ Show your work, including values for $c$ and $n_0.$

$(1)T(n)=10$

$(2)T(n)=2n^3+1$

$(3)T(n)=n^4+2n^2+nlogn$

$(4)T(n)=log(52^n)$

$(5)T(n)=3n^{2}logn$