Recent content by physics604

I'm assuming they did something like this? $$\int \frac{-du}{u+1} = -\frac{1}{1}\ln {|u+1|} +C$$

How was she able to ln the instead like that? I thought there was a factor of \frac{1}{a} to deal with?

1. $$\int \frac{1}{1+e^x}\,dx$$ Homework Equations Substitution The Attempt at a Solution $$u=1+e^x$$ $$du=e^xdx$$ $$\int \frac{1}{u}\frac{1}{e^x}\,du$$ $$\int \frac{1}{u}\frac{1}{u-1}\,du$$ $$\int \frac{1}{u(u-1)}\,du$$ $$= \ln {|u^2-u|} = \ln {|(1+e^x)-(1+e^x)|} = \ln...

Oh, I got it now. Thanks! My integral would be $$\int e^u\,du$$

∫ex+exdx=∫exeexdx=∫ueudu Do you mean I should do something like this? $$\int e^x\,dx = \int e^xe^{e^x}\,dx = \int ue^u\,e^x dx$$ But the point of my substitution was to turn everything into u's...

$$du=e^xdx$$ How does this work into the calculation?

1. $$\int e^{x+e^x}\,dx$$ Homework Equations Substitution, integration by parts The Attempt at a Solution $$u=e^x$$ $$\int e^{x+e^x}\,dx = \int e^x e^{e^x}\,dx = \int ue^u\,du$$ $$a=u$$ $$da=1du$$ $$dv=e^udu$$ $$v=e^u$$ $$=ue^u-\int e^u\,du = ue^u-e^u$$ $$=e^x e^{e^x}+e^{e^x} =...

1. If the function f(x)=x3+a2+bx has the local minimum value at \frac{-2}{9}\sqrt{3}, what are the values of and a and b? Homework Equations $$f'(x)=0$$ The Attempt at a Solution I automatically took the derivative, getting $$f'(x)=3x^2+2ax+b$$ However, I have no idea where to go from...

1. Find a cubic function f(x)=ax3+bx2+cx+d that has a local maximum value of 3 at x=-2 and a local minimum value of 0 at x=1. Homework Equations $$f'(x)=0$$ The Attempt at a Solution The first thing I did was taking the derivative of f(x). $$f'(x)=3ax^2+2bx+c$$ I know that you can get the...

Sorry, I meant all values of x have to be greater than 0. I'm taking Calculus AB in school and we don't cover L'Hopital's Rule in that course. My modified function was the alternate method that my teacher taught us. He said that we should divide everything by the largest degree of x so that we...

1. $$f(x)=x-\frac{1}{6}x^2-\frac{2}{3} lnx$$ Homework Equations limits The Attempt at a Solution I know there is a vertical asymptote at x=0 because all values of x have to be greater than x. The answer says that there is no horizontal asymptote, but I don't know how it...

I checked the time derivative of x=tany but I still get $$\frac{dx}{dt}=sec^2θ×\frac{dθ}{dt}×y$$ I've also attached a drawing.

1. A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is \frac{\pi}{3}, this angle is decreasing at a rate of -\frac{\pi}{3} rad/min. How fast is the plane traveling at that time? Homework Equations...

Sorry that was just a typo. The work should still follow r=h/2.

$$cosθ(t)×\frac{dθ}{dt}?$$