Friday, January 25, 2019

calculus - Limits without L'Hopitals Rule

Evaluate the limit without using L'hopital's rule


a)$$\lim_{x \to 0} \frac {(1+2x)^{1/3}-1}{x} $$


I got the answer as $l=\frac 23$... but I used L'hopitals rule for that... How can I do it another way?


b)$$\lim_{x \to 5^-} \frac {e^x}{(x-5)^3}$$


$l=-\infty$


c)$$\lim_{x \to \frac {\pi} 2} \frac{\sin x}{\cos^2x} - \tan^2 x$$


I don't know how to work with this at all


So basically I was able to find most of the limits through L'Hopitals Rule... BUT how do I find the limits without using his rule?

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