Recent content by Bueno

I think things are clear now. In the other case: $$\int_0^x\sqrt{|tan(w)|} dw$$ The first derivative would be: $$\frac{d}{dx} \int_0^x\sqrt{|tan(w)|} dw = \sqrt{|tan(x)|} $$ Am I right? If so, how to calculate the second derivative? When I came across other functions involving absolute...

I'm sorry, but I didn't understand what you mean by "where the function starts". When I'm plotting this graph, the lower limit tells me where I should start?

It does not have any real root, so there are no critical points. It doesn't make sense for x < 0 and is always positive in it's domain (which seems to be $$(0, +\infty)$$ The second derivative is: $$\frac{e^{x} (2x - 1)}{4x^{3/2}}$$ What gives us the inflection point $$(\frac{1}{2}; 0)$$ It...

Then, the result would be: $$e^{x} 1/2\sqrt{x}$$ ?

But where? I mean, what is the function I should calculate the derivative first? In the upper limit of integration ($$\sqrt{x}$$)? Or $$e^{t^2}$$ ?

What a mess! I think I "mixed" some Xs and Ts during the calculations. I've never hear about this form of the FTOC, but after some researches I came across this definition:"Let f be a continuous function and let a be a constant. Then the function $$ G(x) := \int_a^x f(t)dt$$ is differentiable...

I thought of something like this: I don't know if I really have to take into account the limits of integration to find the derivative of this function. If I have to, I thought of something about the upper limit: This integral is a function $$G(x)$$, then, we have $$G(\sqrt{x})$$, so...

Hi, how are you? I came across some exercises that really puzzled me. They ask me to graph the following functions: $$ a) \int_0^x\sqrt{|tan(w)|} dw $$ $$ b)\int_0^\sqrt{x} e^{t^2}$$I imagine I'll have to use derivative techniques as I would when graphing a "normal" function, but those...

I couldn't see anything like this, it worked perfectly. It's the first limit I see that needs this kind of trick. Thank you! I've been studying this kind of limits today and most of them were solved by the technique I mentioned in the first post, except for the one you just showed me how to...

I've been studying this kind of limits today and most of them were solved by the technique I mentioned in my previous topic, except for the one you just showed me how to solve and this one: $$\lim_{x->0} (1 - cos(x))^{1/x}$$ (It approaches 0 from the left, but I don't know how to write it...

Hello everyone, how are you? I'm having trouble to evalue the following limit: $$\lim_{x->\infty} (\frac{x}{1+x^2})^x $$ I "transformed" it into $$e^{ln{(\frac{x}{1+x^2})^x}}$$ and tried to solve this limit: $$\lim_{x->\infty} x ln{(\frac{x}{1+x^2})}$$ But I have no idea how to solve it...

That seems to work, thank you! But I have to say I'm a bit confused by this kind of proof. Choosing an appropriate value for delta seems to do the work, but is there any kind of manipulation or technique I can do to make the value I have do choose become more clear? Thank you, Bueno

The main problem is I can't use derivative techniques to solve this problem. The professor only talked about limits and their properties in class, and he'd like we figure out how to prove this only using these tools. Thank you, Bueno

Hello everyone! I'm having some trouble to solve the following exercise: Supposing that $$|f(x) - f(1)|≤ (x - 1)^2$$ for every $$x $$. Show that $$f$$ is continuous at $$ 1$$ (Sorry if the text seems a bit weird, but it's because I'm still getting used to translate all these math-related...