Analysis and Calculus

Can someone give me an example of a bijection between [math]\mathbb{R}[/math] and [math][0,1][/math]

is divergent, but my professor said the proof wasn't in the sillibus. I'm sure anyone here could show me why. Please?

I don't know how to solve this one. Can anyone help me? A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks from the pole with a speed of 5ft/s along the straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?

I need to simplify and solve. Could u plz gimme a step by step answer bcuz i get very confused in these type of cubed root questions. lim ((x+27)^1/3) -3) / x x->0 Its x+27 all under a cubed root subtract 3, all of this divided by x. Thanks in advance

Here's a tricky optimization problem. I'm having a hard time figuring it out and it's driving me CrAzY!! I know that I have to set the first derivative equal to zero to find the minimum; my problem is figuring out the equations involved. Anyone have any ideas? I'm getting really frustrated with it. The wreck of a plane in a desert is 18 miles from the nearest point "A" on a straight road. A truck starts for the wreck at a point on the road that is 40 miles distant from A. If the truck can travel at 70mph on the road and at 35mph on a straight path in the desert, how far from point "A" should the truck leave the road to reach the wreck in minimum time?

Just wondering why calculus? I dont know much about this subject, just interested. What are some examples of real-life situations where u would need calculus? I also heard that Cal 3 incorporates many dimensions.... explain!

You have a triangle with two fixed sides of 12 and 15 meters. the angle between them is increasing at 2 Degrees per min. how fast is the opposite side increasing in length when the angle is 60 degrees? i figure it's cos law but i don't know how to continue, or if it is even cos law.

I'm not sure if this belongs here or in the homework section, but, I'm looking for an online resource of problems for a differential calculus class (derivatives, optimization, related rates, etc.). I've google'd it and found a few, but a lot are dead links or only have one or two problems, and a whole lot of explanations. I'm just looking for problems, with answers. I thought someone here might be kind enough to point me in that direction. Thanks in advance:)

What does the limit indicate for? Like lim x=pi/2. Does it mean only x value less or equal to pi/2? Also, what does Devrivates mean? Give me examples won't hurt. Thanks

Hi all, I'm trying to solve this differential equation but I'm getting strange results. Don't know how type all the symbols so I hope it makes sense. dy/dx + 3y = 6 dy/dx = 6 - 3y 1/(6 - 3y)(dy/dx) = 1 1/(6 -3y)dy = dx if I integrate both sides (-1/3 )ln[6-3y] = x + C boundary cond. when y=3 x=0 to find C, I substitute (-1/3)ln[6-3(3)] = C ok, this is where I'm stuck. Do I take C to be zero in this case. Also, does anyone know of a website where I can get a simple and easy introduction to first order linear differential equations? Thanks

Right now in calculus we're doing related rates, specifically to do with triangles and the useage of Pythagorean Theorem. The problem goes like this: A police helicopter is flying north at 60km/h at a constant altitude of 1 km. On the highway below, a car is travelling east at 45 km/h. When the chopper passes over the highway, the car is 2 km west of the point directly below it. At this moment, how fast is the distance between the car and the chopper changing? Is this distance increasing or decreasing? Explain. Now the answer they give in the back is 40.25 km/h and they say it's decreasing. I figured this out so far with c being the distance the car travel…

If A is Lebesgue measurable and x is an element of Rn, then the translation of A by x, defined by A + x = {a + x : a ∈ A}, is also Lebesgue measurable and has the same measure as A.

Hi guys! In calculus, we were shown ways of finding maximums and minimums. To do this, we had to differentiate, and then make the differential=0. Then, to make sure whether is was a maximum or minimum, we double differentiated the original equation (or simply differentiate the differential). If the value was positive, the point was a local minimum, and vice versa. The book had stated that if the double differential was equal to 0, then, it was a point of inflexion. However, my teacher stated that this does not apply on some curves, and therefore, not to use it, but find the gradient before and after the point, and decide thereon. Could some of you guys please …

Hey guys, I could use some help with these problems: (I don't know how to get any of the symbols so bear with me) integral from 0 to pi/4 of cos^4(4x)sin(4x)dx integral(x^3-5x+2)/(x^2+49)dx integral 2x^3squareroot(25+36x^2)dx integral sin^2(5x)cos^5(5x)dx integral sin^2(6x)cos^2(6x)dx Any kind of help and/or solutions would be appreciated here.

What is an additive identities? (e.g. sin(a+b))? Then what is a double angle identities? e.g. sin(2x) sin(x + x) would be the right answer? But how does double angle identity applies to it?

this equation 2sin(x)cos(x) the derivative of that is 2cos(2x) but on my TI-89 it gives me 4(cos(x))^2-2 when plug in an integer, same output answer........ someone show me that they are equal

so, I'm having a hard time with path independance, namely with how do you find the scalar function that your vector function is the gradient of. or G in (nabla)G = f

I am unsure which is correct: e.g. [math] y = \cos2(x-\pi)+3 [/math] Can it be defined as [math]y=\cos(2x-2\pi)+3[/math]? Following the basic equation of y = AsinB(x-c)+D, does the above example means it have an vertical translation of 2 and phase shift of 2pi to the right? [i know the graph will appear the exact same regardless, but I want to know which equation is more correct to draw graphs.]

Hi all how is everyone hope good and fine i am new here but really a good forum which share very very big and important knowlegde a small problem face me in get a solution for the question: -if tangent line to the ellipse 9x^2 + 4y^2 = 36 has y intercept 6 find the equation of the tangent. the problem is when we substitute y by 6 and try to get a value for x the equation will be as follow x^2 = -12 the problem is there is no roots for a negative number otherwise we use an imaginry numbers hope anyone could help me to a get a solution for that question thanks in advance

Can someone help me on these two questions... you must find the first two derivatives of f(x)... first: f(x)= -cot(x) I think I've got the first one... f'(x)= csc^2(x) but I'm lost on the second derivative. Next Question: f(x)= sec(x) - csc(x) again, I think I've got the first one... f'(x)= sec(x)tan(x) + csc(x)cot(x) but f''(x)= ??? Thanks.

Find the derivative of [Math]x^{1/3}[/Math] by the first principle. May anyone show me the steps?

Can someone help me find the volume of a torus? I understand how to find volume with the integral, but the torus is giving me sufficient trouble. Worse yet, the calculus teacher at my school refuses to answer my questions because I'm not in his calculus class.

Hey guys i had this problem that i want an explanation for. I want a good way to solve it probably using limits or some part of calculus. Can anyone find a good way ot figure it out? Here's the problem: (TESTS YOUR INTELLIGENCE) Two cities A and B are connected by a 100 mile railroad. In each city there is a train. At one instant the trains start moving toward each other with equal speed of 50 mph. Train A had a fly sitting on it, which took off at the moment of the train's departure and started flying toward train B with a speed of 90 mph. When the fly reached train B it turned around and started flying toward train A at 90 mph. The fly bounced betwe…

1) Find [math] \frac{d}{dx} log(lnx) [/math] I assume that the log has a base of 10, so I got [math] \frac{1}{x(lnxln10)} [/math] 2) Find the slope of the line tangent to the graph [math] cos(xy)=y [/math] at [math] (0,1) [/math] [math] -sin(xy)(y)+(xy')=y' [/math] [math] -ysin(xy)=y'-(xy') [/math] [math] \frac{-ysin(xy)}{1-x}=y' [/math] Then I just keep getting 0 when I substitute (0,1) in... 3) If [math] y=(lnx)^{sinx} x>1, [/math] Find [math] y' [/math] [math] sinxlnx=sinx\frac{1}{x}+(cosx)(lnx) [/math] [math] \frac{sinx}{x} +cosxlnx [/math] [math] 1+cosxlnx [/math]

I have a couple questions about plotting a curve with assymptotic limits. 1) Suppose you had the equation y = x^2. The domain for x is [-infinity, +infinity]. Therefore, there is no vertical assymptote. How would you have to modify the equation such that there is an vertical asymptote? Would it have to be a totally different equation? Obviously, it needs to be an exponentially increasing/decreasing curve (let's stick with increasing though). 2) Supposing you did modify the equation such that there was a vertical asymptote. What would you have to do to adjust where along the x-axis this asymptote intersected?