$(3)$ Calculate $\underset{x-1}{lim}\frac{2x^2+3x+1}{x^2-x-2}$

$(4)$ Calculate $\underset{x2}{lim}\frac{x^2+x-6}{1-\sqrt[\phantom{2}]{x-1}}$

$(5)$ Calculate $\underset{x0}{lim}\frac{2x^2+3x}{sin(3x^2-4x)}$

$(6)$ Let $f(x)=\frac{x^2+2x-3}{x^2-6x+5}$

$($a$)$ Find all points where the function is not continuous. Explain why the function is not continuous there.

$($b$)$ For which of those points is the discontinuity removable? Explain how to remove it$.$

$(7)$ Using the definition of derivative, calculate the derivative of $f(x)=3x^2-2x+1.$

$(8)$ Using the definition of derivative, calculate the derivative of $f(x)=\sqrt[\phantom{2}]{3-2x}.$

For the following derivatives, include your work and do not simplify the answer.

$(9)$ Calculate the derivative of $f(x)=6x^3-3x^2+2x-4lnx+\frac{2}{x}.$

$(10)$ Calculate the derivative of $f(x)=2x^5-4x^2+3e^x-\frac{4}{x^2}+3\sqrt[\phantom{2}]{x}.$