Calculating the limits without the L'Hospital rule

[mathmari]

Hey!

How could we calculate the following limits without the L'Hospital rule?

$$\lim_{x\rightarrow 0}\frac{\sin (x)-x+x^3}{x^3} \\ \lim_{x\rightarrow 0}\frac{e^x-\sin (x)-1}{x^2}$$

Is the only way using the Taylor expansion? (Wondering)

 

[Opalg]

Hey!

How could we calculate the following limits without the L'Hospital rule?

$$\lim_{x\rightarrow 0}\frac{\sin (x)-x+x^3}{x^3} \\ \lim_{x\rightarrow 0}\frac{e^x-\sin (x)-1}{x^2}$$

Is the only way using the Taylor expansion? (Wondering)

It certainly looks as though they are expecting you to use the Taylor series expansions for the sine and exponential functions.

 

[mathmari]

Ah ok... Couldn't we use for example the squeeze theorem? (Wondering)