1. ## Ridiculous Calculus Test

Hey,
I am new to the forum so I am not sure on how this works... but I am in desperate need of help for my test.

We have covered all the way up to integrals, so if you know any methods to solve the following problems that are beyond integrals aren't acceptable.

Any hints/solutions/steps help. Thank you.

1) Prove that | tan x + tan y | >/ | x + y |
---(prove that the absolute value of (tan x + tan y) is greather than or equal to absolute value of (x + y) )

2) f(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e, where 2a^2 < 5b,
show that equation f(x) = 0 can't have more than three distinct real solutions (roots)

3) A light is at the top of a 16 ft. light pole. A boy 5 ft. tall walks away from the pole at the rate of 4ft/sec.
-a) at what rate is the tip of his shadow moving when he is 18ft. from the pole?
-b) at what rate is the length of his shadow increasing?

4) a rocket is rising vertically at 880 ft/sec. there is a camera on the ground recording the event. when it is 4000 ft up, how fast is the camera to rocket distance is changing at that instance? How fast must the camera's elevation angle change at that instance to keep the rocket in sight?

5) use newton's method to prove: e^x = 3-2x

6) find dy/dx if 2y^3 + (t^3)(y) = 1 and dt/dx = 1/cos t

There are plenty more, but let's start there.
Thank you so much for anyone that can help!

2. Originally Posted by zizour10
Hey,
I am new to the forum so I am not sure on how this works... but I am in desperate need of help for my test.

We have covered all the way up to integrals, so if you know any methods to solve the following problems that are beyond integrals aren't acceptable.

Any hints/solutions/steps help. Thank you.

1) Prove that | tan x + tan y | >/ | x + y |
---(prove that the absolute value of (tan x + tan y) is greather than or equal to absolute value of (x + y) )

2) f(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e, where 2a^2 < 5b,
show that equation f(x) = 0 can't have more than three distinct real solutions (roots)

3) A light is at the top of a 16 ft. light pole. A boy 5 ft. tall walks away from the pole at the rate of 4ft/sec.
-a) at what rate is the tip of his shadow moving when he is 18ft. from the pole?
-b) at what rate is the length of his shadow increasing?

4) a rocket is rising vertically at 880 ft/sec. there is a camera on the ground recording the event. when it is 4000 ft up, how fast is the camera to rocket distance is changing at that instance? How fast must the camera's elevation angle change at that instance to keep the rocket in sight?

5) use newton's method to prove: e^x = 3-2x

6) find dy/dx if 2y^3 + (t^3)(y) = 1 and dt/dx = 1/cos t

There are plenty more, but let's start there.
Thank you so much for anyone that can help!
Instead of asking for help on all the individual questions, why don't you break down the problem, ask yourself what's happening and what you'll need to solve it. Then try. If you get stuck after trying, show us your work and where you're stuck, then we can help.

Also, is this an actual take home exam? If so we cannot knowingly help you.

3. It is only a homework. I figured to put "test" in the title to emphasize its importance. And the homework is about 25 problems, all about the same difficulty. I've done most of them but these (and just a few more) are the ones where I don't know where to even start.