MATH218 TEST

Find the following limit:

 $\lim_{x\rightarrow-3}\left(\frac{x^2+x-6}{x+3}\right)$  

• 6

• -5

• 1

• -2

Find the following limits:

 $\lim_{x\rightarrow-2}\left(\frac{3-\sqrt{1-4x}}{2x+4}\right)$  

•  $\frac{1}{3}$  

• 0

•  $8$  

• -2

Find the following limit:

 $\lim_{x\rightarrow\infty}\left(\frac{5x^8-9}{x^3+10x^5-3x^8}\right)$  

• 0

•  $\frac{5}{-3}$  

• Does not exist

•  $-\infty$  

Differentiate the following function: $f\left(t\right)=\frac{2}{3t^9}+\frac{1}{7t^3}-9t^2-\sqrt{t^3}$  

•  $f'\left(x\right)=-\frac{6}{t^{10}}+\frac{3}{7t^4}-18t+\frac{3\sqrt{t}}{2}$  

•  $f'\left(x\right)=\frac{6}{t^8}-\frac{3}{7t^3}-18t-\frac{\sqrt{t}}{2}$  

•  $f'\left(x\right)=7t^4-18t-\frac{3\sqrt{t}}{2}$  

•  $f'\left(x\right)=-\frac{6}{t^{10}}-\frac{3}{7t^4}-18t-\frac{3\sqrt{t}}{2}$  

Differentiate the following function: $h\left(v\right)=\ln\left(e^v\cos\left(v\right)\right)$  

•  $h'\left(v\right)=\frac{1}{e^v\cos\left(v\right)}\left[e^v\cos\left(v\right)+e^v\sin\left(v\right)\right]$  

•  $h'\left(v\right)=e^v\cos\left(v\right)$  

•  $h'\left(v\right)=1-\tan\left(v\right)$  

•  $h'\left(v\right)=\frac{1}{e^v\cos\left(v\right)}$  

Find the equation to the tangent to the curve  $y=\frac{3}{\sqrt{2x-3}}$  at x=2.

•  $t=-3x+9$  

•  $t=3x-6$  

•  $t=3x+9$  

•  $t=3x$