# Questions tagged [limits-without-lhopital]

The evaluation of limits without the usage of L'Hôpital's rule.

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### Solving this limit without L'hopital's

I'm having a problem with limits, I'm just getting started to learn them but we didn't cover the limits of trig functions nor did we cover l'hopital's rule as we didn't cover derivatives yet, how can ...
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### Prove/Find limes without L'Hospital [closed]

I would like to understand limits more on the basis of the fundamental definitions. So can someone please help me to prove the following limit without L'Hospital? Unfortunately, I have no approach at ...
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### Limit of the indeterminant form [closed]

I was trying to understand the limit of the following function for $a > 1$ and $0 <b < 1$. \begin{align} \lim_{x \rightarrow 0} x^b a^{log_2(1/x)} \end{align}. This is an indeterminate ...
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### Removing Intermediate forms using Integration [duplicate]

As we know that using L'hospital rule rule we can differentiate the numerator and denominator separately to remove the Intermediate form. For example $$\lim_{x\to 0}{\frac{e^x-1}{x^2+x}}$$ So my doubt ...
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1 vote
1 answer
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### Finding the limit of an equation involving the Gaussian?

Here's a math competition problem that I've been stumped on I tried using L-Hopital's rule, I see how we get the equivalence via the M.V.T., but that approach doesn't seem to be working at all. I'm ...
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### Proving $\lim_{x\to\infty}xa^{x}=0$ in Elementary Ways

I wish to prove the following limit without using L'Hopital rule or other known limits: $$\lim_{x\to\infty}xa^{x}=0$$ where $0<a<1$. I wanted to do so using this sequence limit (which I know how ...
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1 vote
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### Is this a correct approach to calculating $\lim_{n\rightarrow \infty} {\sqrt[n]{\ln(n)}}$?

We have just started covering the limit of sequences and I've stumbled upon this limit in our uni's excercises: $$\lim_{n\rightarrow \infty} {\sqrt[n]{\ln(n)}}$$ I've considered solving it using the ...
1 vote
1 answer
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4 answers
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