Home school Calculas( high school level)

In summary, the conversation is about a user seeking help with solving math problems for an exam. The problems involve finding derivatives, tangents, asymptotes, and solving equations. The user also asked for help with a helicopter-related question. Some mistakes were made in the solutions provided, and other users helped to correct them.
  • #1
Stupid_neko
3
0
Hi.. New at this site, hope I'm posting these stuff on the write place...
well i had these question below for review for an exam, hope someone can help me solve them, i did my solution in Paint program and on paper and am linking where i uploaded them, ( image shack)

-Find the second derivative
1)y=2x^3e^4x
solution
http://img519.imageshack.us/img519/1610/pictureorvideo004sf6.th.jpg [Broken]

2)y=√(x^3+e^-x+5)
** for where 'e^-x' i think the question is wrong,, i think it should be e^x, not sure??
solution
http://img340.imageshack.us/img340/6392/pictureorvideo005fp2.th.jpg [Broken]

3)Find the second derivative of 'y' with respect to "x" where
y=x^2/X^2
solution
http://img340.imageshack.us/img340/6238/pictureorvideo007rt7.th.jpg [Broken]

4)Find the equation of 2 lines, each of slope 5, that are tangent to y=x^3+2X

5) Find the asymptotes for
f(x)=x/√(4x-1)

6)A dragster accelerates down a strip adn then brakes, adn comes to stop. Its position function, s(t) is given by s(t)=3t^2-1/5t^3, s'(t) in meters, 't' in seconds
a) when does the dragster come to a stop
b) how far has the dragster traveled.
Solution
http://img340.imageshack.us/img340/8870/5aso0.th.png [Broken]

7) Find the polynomial with second degree that goes through (1,-1) and whose slope is 1, When x=-1 and where slop is 19, when x=2
solution
http://img457.imageshack.us/img457/3368/pictureorvideo003mp2.th.jpg [Broken]


8) A helicopter takes off from landing pad at 10:48AM and travels south at 150KM/h is planning to land at 10:56AM.
a) how far is the distance between them changing at 10:50AM( to 2 decimal place)
b) Is the distance between them increasing or decreasing at this instant?


I couldn't answer 4,5,8... please help me with them...and check solution
thank you ...
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
For #4, the derivative is a quadratic. There are 2 places where the tan line has a slope of 5. Find the points where it equals 5 (or where that minus 5 equals zero) and then you have 2 points and 2 slopes
 
  • #3
8. If he's traveling at 150 km/h, then that's how fast the distance is changing. For b, it depends. If it went past his destination before 10:50, then the distance is increasing, otherwise it's decreasing.
 
  • #4
turdferguson said:
For #4, the derivative is a quadratic. There are 2 places where the tan line has a slope of 5. Find the points where it equals 5 (or where that minus 5 equals zero) and then you have 2 points and 2 slopes

For quadratic equation i would need a,b and c. but i have only 2 numbers...and how would i find the point where the point equals 5?


Also can anyone check the solutions i did,

thanks
 
  • #5
"For quadratic equation i would need a,b and c. but i have only 2 numbers...and how would i find the point where the point equals 5? "
A "point" can't equal 5! You are looking for the value of x such that the derivative 3x2+ 2= 5. Surely you can solve that equation.
 
  • #6
For #1 the final answer(first derivative) is [tex](e^{4x} \cdot 2x^2) \cdot (4x+3)[/tex] not 2x + 3...you multiplyed by 2 insted 4...

Edit...even more simple it is if you leave it like this [tex]6x^2 e^{4x} + 8x^3 e^{4x}[/tex] and make a second derivative...
 
Last edited:
  • #7
sstone said:
Edit...even more simple it is if you leave it like this [tex]6x^2 e^{4x} + 8x^3 e^{4x}[/tex] and make a second derivative...

I factored out the 2x^2, if you factor it back in , you get the same result...So confused,,,dont know where i made mistake sorry sorry,,,,,,,could you show me where i made the mistake,,,

thank you everyone for your help:)
 
  • #8
You multiplied it wrongly...
pictureorv104wr.jpg
 

What is calculus and why is it important to learn in high school?

Calculus is a branch of mathematics that deals with rates of change and accumulation. It is important to learn in high school because it lays the foundation for advanced mathematics and science courses, and is also used in fields such as engineering, economics, and computer science.

Is homeschooling a viable option for learning calculus at the high school level?

Yes, homeschooling can be a viable option for learning calculus at the high school level. There are many resources available, such as textbooks, online courses, and tutors, that can help students learn and understand the concepts of calculus.

Do I need to have a strong background in math to learn calculus at the high school level?

Having a strong foundation in algebra and trigonometry is helpful, but not necessarily required to learn calculus at the high school level. As long as you are willing to put in the time and effort to learn, you can succeed in calculus.

What are the key topics covered in high school level calculus?

The key topics covered in high school level calculus include limits, derivatives, integrals, and applications of derivatives and integrals. These concepts build upon each other and are essential for understanding calculus.

How can I make sure I am understanding and retaining the concepts of calculus while homeschooling?

It is important to regularly practice and review the concepts covered in calculus. This can be done through solving practice problems, taking online quizzes, and seeking help from tutors or online resources. It is also helpful to create a study schedule and stick to it to ensure consistent learning and retention of the material.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
515
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
3K
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
746
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
17
Views
3K
Replies
13
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
8K
Back
Top