Mathematics - Limits Question with Solution | TestHub

We know that,

The slope of line $45x+5y+3=0$ will be $-9$

Now, given $27r_1+\frac{9r_2}{2}=-9$

Now, solving

$L=\underset{x\to 3}{\lim }\frac{{\int }_3^{x}8t^{2}dt}{\frac{3r_{2}x}{2}-r_2{x}^2-r_1{x}^3-3x}$

Applying Newton Leibnitz Theorem and L'Hospital Rule we get,

$\Rightarrow L=\underset{x\to 3}{\lim }\frac{8x^2}{\frac{3r_2^{}}{2}-2r_{2}x-3r_1{x}^2-3}$

$\Rightarrow L=\frac{72}{\frac{3r_2}{2}-6r_2-27r_1-3}$

$\Rightarrow L=\frac{72}{-\frac{9r_2}{2}-27r_1-3}$

Now, using $27r_1+\frac{9r_2}{2}=-9$ we get,

$\Rightarrow L=\frac{72}{9-3}=12$