$17\right)$ Prove that $p.\left($ $\left(\dfrac {f\left(r\right)} {r}x\right)=\dfrac {1} {r^{2}}\dfrac {d} {dr}\left(r^{2}f\right)ar$ and $θ^{2}f\left(r\right)=\dfrac {d^{2}f} {dr^{2}}+\dfrac {2} {r}\dfrac {df} {dr}$ where $f\left(r\right)$ is a scalar function having continuous derivatives, $r=xi+yi+zk$ and $r=\left(x^{2}+$ $-y^{2}+z^{2}\right)\dfrac {1} {2}$

Prove that the sequence $\left(a_{n}3,$ where $q_{a}$ $=\dfrac {2n-1} {3n+5}$ converges to $\dfrac {2} {3}$ $\sqrt{4+} ,$ prove that

In the following problem $a,b,$ b,and c represent REAL NUMBERS. The derivative of $g\left(x\right)=log _{a}\left(bx\right)+cx^{2}is$ $○$ $g^{1}\left(x\right)=\right)dfrac\left(b\right)log _{-}a\left(bx\right)\right)\left(N1n$ $a\right)+2cx1\right)$ $○$ $\left(g\left(x\right)=\right)dtracb$ $loga\left(bx\right)+2c\times \right)Nln$ a}\) $○$ $g^{'}\left(x\right)=\left(dfraC\left(a\right)log _{-}a\left(bx\right)\right)\left(ln$ $\right)+2c\times 1\right)\right)$ $○$ $g^{1}\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(ln$ $a1\right)$ $○$ $\left(\left(g^{1}\left(x\right)=b$ $log _{-}a\left(bx\right)+2cx1\right)$ $○$ $g\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(1ln$ $a|+2c1\right)$