Science:Math Exam Resources/Courses/MATH100/December 2012/Question 06 (e)

MATH100 December 2012

  •  Q1 (a)  •  Q1 (b)  •  Q1 (c)  •  Q2 (a)  •  Q2 (b)  •  Q2 (c)  •  Q2 (d)  •  Q3 (a)  •  Q3 (b)  •  Q3 (c)  •  Q4 (a)  •  Q4 (b)  •  Q4 (c)  •  Q5 (a)  •  Q5 (b)  •  Q6 (a)  •  Q6 (b)  •  Q6 (c)  •  Q6 (d)  •  Q6 (e)  •  Q6 (f)  •  Q7  •  Q8  •  Q9  •  Q10  •  Q11  •  

   Other MATH100 Exams

  •  December 2011  •  December 2010  •  December 2012  •  December 2013  •  December 2014  •  December 2015  •  December 2016  •  December 2018  •  

Question 06 (e)

Full-Solution Problems. In questions 5-11, justify your answers and show all your work. If a box is provided, write your final answer there. Unless otherwise indicated, simplification of numerical answers is required in these questions. 6. Let $f(x)=2x^{3/5}+3x^{-2/5}$. Note that the domain of ƒ is the set of all nonzero real numbers; for example, $f(-1)=-2+3=1$. (e) Find all vertical asymptotes of the graph $y=f(x)$.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Check points of the function where it is not continuous and verify that one of the left or right hand limits are positive or negative infinity.

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. As given in the original statement, the function has domain of all nonzero reals. The function itself is only not continuous at 0 so we check there for an asymptote. The value ${\begin{aligned}\lim _{x\to 0^{+}}(2x^{3/5}+3x^{-2/5})=\infty \end{aligned}}$ since this function when we plug in values of x slightly bigger than 0, the first term tends to 0 and the second term tends to positive infinity. Notice that the left hand limit is also positive infinity since the second term can be written as $\displaystyle 3x^{-2/5}={\frac {3}{\sqrt[{5}]{x^{2}}}}$ which is always positive.

Click here for similar questions

MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Asymptote, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag