Given the complexity g$($n$)=9$n$^7+5$n$^3+2$n$^4$ log$($n$).$

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a$)(5$pt$)$ try to find its Big$-$oh notation.$($Hints: use the conclusions covered in the lecture notes$)$

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b$)(5$pt$)$ try to prove that O$($n$^8)$ is an overestimate for g$($n$)($Hints: use the limit techniques and check the value of this limit$).$ You can prove it using math or write a short code using different Ns$.$