Calculation of function limits

Compute the following limits:

a) $\displaystyle\lim_{x \to 0}{((2x+1)\cdot\dfrac{x^2-x}{x})}$

b) $\displaystyle\lim_{x \to -3}{x^3+x^2-x}$

c) $\displaystyle\lim_{x \to -\infty}{x^4+2x^2}$

We are going to solve the following limits using the properties of limits that we already know:

a) $\displaystyle\lim_{x \to 0}{((2x+1)\cdot\dfrac{x^2-x}{x})}=\lim_{x \to 0}{(2x+1)}\cdot\lim_{x \to 0}{\dfrac{x^2-x}{x}}=$

$$\displaystyle=(2\cdot0+1)\cdot\lim_{x \to 0}{\dfrac{x(x-1)}{x}}=1\cdot\lim_{x \to 0}{x-1}=1\cdot(-1)=-1$$

b) $\displaystyle\lim_{x \to -3}{x^3+x^2-x}=(-3)^3+(-3)^2-(-3)=-27+9+3=-15$

c) $\displaystyle\lim_{x \to -\infty}{x^4+2x^2}=(-\infty)^4+2\cdot(-\infty)^2=+\infty+2\infty=+\infty$

a) $-1$

b) $-15$

c) $+\infty$