Calculate the value

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}\) 
$○$ $g^{'}\left(x\right)=\left(dfraC\left(a\right)log _{-}a\left(bx\right)\right)\left(ln$ $\right)+2c\times 1\right)\right)$ 
$○$ $g^{1}\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(ln$ $a1\right)$ 
$○$ $\left(\left(g^{1}\left(x\right)=b$ $log _{-}a\left(bx\right)+2cx1\right)$ 
$○$ $g\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(1ln$ $a|+2c1\right)$ 

Question $4$ 
If $x$ is $6$ what $|s$ 
$\dfrac {1} {3}x$ 
$1frac\left(1\right)\left(3\right)x$ 

Tovah solves the equation $\square 1aTex$ $ltac\left(1\right)\left(x+3\right)+lirac\left(2\right)\left(x\right)=ltrac\left(3\right)\left(x+3\right)$ $an0$ 
obtains $-1aTe\times $ $x\right):=-3:\right):x\left(:=1:0$ 
Determine if $21a$ $aTex:$ $x\right):=:-3$ $:or\left(:x\right):=0$ extraneous. Justify your answer. 
$On|yx=-3$ is extraneous and $x=0isa$ real solution. 
$○$ $Onbyx=0$ is extraneous and $x=-3is$ real solution. 
$○$ Both solutions are extraneous because when $x=-3$ and $x=0$ are substituted into the original 
equation, it makes a denominator equal to zero and you canhot divide by 0 (undefined). 
$○$ O Both $x=-3andx=0$ are real solutions. There are no extraneous roots. 

$\left(int|imits$ $-0a1\left(1-\times n_{2}{\right)_{3}}^{n}$ 
$x^{A}3dx=7\right)$ 
$\left($ $frac\left(1\right)\left(40\right)\right)$ 
$\left($ $\left(troc\left(1\right)\left(35\right)\right)$ 
$\left(troc\left(1\right)\left(30\right)\right)$ 
$\left(tr0c\left(1\right)\left(25\right)\right)$ 

$11.$ Question $11$ 
Solve the $:$ $folloMlng'$ $0<θ<90^{°}$ 
$\left(1\right)$ $2sin^{2}θ=1\right)$ $\left(rac\left(3\right)\left(2\right)\right)$ 
$\left(11\right)$ $3tan^{2}θ+2=3$ 
$\left(111\right)cos^{2}θ$ $11rac\left(1\right)\left(4\right)\right)=$ 
$c\left(1\right)\left(4\right)\right)=11113c\left(1\right)\left(2\right)\right)$ 

Which of the following rational numbers are 
equivalent? 
$0Ptionsy$ 
A \frac{5}{6}, \frac{30}{36} 
B $s\sqrt{rac\left(} -2\right)\left(3\right)\sqrt{1rac} \sqrt{4\right)16\right)4} $ 
C $s\sqrt{11aC\left(} -4\right)1-7b,\sqrt{1rac\left(16\sqrt{35\right)9} } $ 
D \frac{1}{2},\frac{3}{8} 

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