I am having hard time evaluating this limit:

I know, that this fact can help

But how? We can transform the first expression to

but what should I do next? I cannot use LHopitals rule for solving this.

Danelle Albright
2022-01-14
Answered

How to evaluate limit without LHospitals rule, but using $\underset{x\to 0}{lim}\frac{\mathrm{sin}x}{x}=1$

I am having hard time evaluating this limit:

$\underset{x\to 0}{lim}\frac{\mathrm{cos}3x-1}{\mathrm{cos}2x-1}$

I know, that this fact can help

$\underset{x\to 0}{lim}\frac{\mathrm{sin}x}{x}=1$

But how? We can transform the first expression to

$\underset{x\to 0}{lim}\frac{\mathrm{cos}3x-1}{-2{\mathrm{sin}}^{2}x}$

but what should I do next? I cannot use LHopitals rule for solving this.

I am having hard time evaluating this limit:

I know, that this fact can help

But how? We can transform the first expression to

but what should I do next? I cannot use LHopitals rule for solving this.

You can still ask an expert for help

Lindsey Gamble

Answered 2022-01-15
Author has **38** answers

sirpsta3u

Answered 2022-01-16
Author has **42** answers

Hint:

It is standard (from the limit of

and you may proceed by substitution.

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Let P(x, y) be the terminal point on the unit circle determined by t. Then

asked 2022-03-23

Solve the equation

$27\mathrm{sin}\left(x\right)\cdot {\mathrm{cos}}^{2}\left(x\right)\cdot {\mathrm{tan}}^{3}\left(x\right)\cdot {\mathrm{cot}}^{4}\left(x\right)\cdot {\mathrm{sec}}^{5}\left(x\right)\cdot {\mathrm{csc}}^{6}\left(x\right)=256$

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How do I prove

$\mathrm{cos}\left(4A\right)={\mathrm{cos}}^{4}A-6{\mathrm{cos}}^{2}A{\mathrm{sin}}^{2}A+{\mathrm{sin}}^{4}A$ ?

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Prove

$\mathrm{sec}\theta +\frac{1}{\mathrm{tan}\left(\theta \right)}=\frac{\mathrm{tan}\left(\theta \right)}{\mathrm{sec}\left(\theta \right)}-1$

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Find:

$\underset{x\to 0}{lim}\frac{\frac{\mathrm{sin}x}{x}-\mathrm{cos}x}{2x(\frac{{e}^{2x}-1}{2x}-1)}$

asked 2022-01-27

Want to do is find out how many solutions there are to the following equation in that interval (here A is a constant): $\mathrm{cos}\left(A\mathrm{cos}\left(\frac{s}{A}\right)\right)=\mathrm{sin}\left(A\mathrm{cos}\left(\frac{s}{A}\right)\right)=A\mathrm{sin}\left(\frac{s}{A}\right),\text{}\text{}\text{}\text{}s\in [0,2A\pi ]$

I know it depends on A and I've tested a few cases, but I'm rusty on this trig stuff, so I haven't been able to do it yet

I know it depends on A and I've tested a few cases, but I'm rusty on this trig stuff, so I haven't been able to do it yet

asked 2022-02-27

Finding all solutions to

${\mathrm{tan}}^{5}x-9\mathrm{tan}x=0$