Problems from Calculation of function limits

Development:

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

a) ${\displaystyle \underset{x\to 0}{lim}((2x+1)\cdot {\displaystyle \frac{x^2-x}{x}})=\underset{x\to 0}{lim}(2x+1)\cdot \underset{x\to 0}{lim}{\displaystyle \frac{x^2-x}{x}}=}$

${\displaystyle =(2\cdot 0+1)\cdot \underset{x\to 0}{lim}{\displaystyle \frac{x(x-1)}{x}}=1\cdot \underset{x\to 0}{lim}x-1=1\cdot (-1)=-1}$

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

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

Solution:

a) $-1$

b) $-15$

c) $+\mathrm{\infty }$

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