Sudibyo G.

Specialist Tutor for Maths, Physics and Chemistry

Tutor Satisfaction Guarantee

Organic Chemistry

TutorMe

Question:

Why $$SOCl_2$$ is used as a preferred reagent to convert alcohol $$R-OH$$ to chloroalkane $$R-Cl$$ rather than $$PCl_5$$?

Sudibyo G.

Answer:

Below is the chemical equation when alcohol reacts with the respective reagents: $$R-OH\ +\ PCl_5 \to \ R-Cl\ +\ HCl\ +\ POCl_3$$ $$R-OH\ +\ SOCl_2 \to \ R-Cl\ +\ HCl +\ SO_2 $$ When using $$SOCl_2$$, the products are gaseous $$\ HCl $$ and $$ SO_2$$, which can easily be cleaned up using pyridine (a base) to obtain a pure sample of $$R-Cl$$ which is the desired end product. On the other hand, the purification of $$R-Cl$$ is more tedious when using $$PCl_5$$.

Pre-Calculus

TutorMe

Question:

How do we know if a function is continuous over a given interval?

Sudibyo G.

Answer:

Basically, there are 3 conditions to check for continuity: 1) If $$f(x)$$ is continuous at a point $$a$$, then $$\lim_{x\to a} f(x)=f(a)$$ 2)if $$f(x)$$ is defined for $$x\geq a$$, then $$\lim_{x\to a^+} f(x)=f(a)$$ 3) 2)if $$f(x)$$ is defined for $$x\leq a$$, then $$\lim_{x\to a^-} f(x)=f(a)$$ This means $$\lim_{x\to a} f(x)=\lim_{x\to a^+} f(x)=\lim_{x\to a^-}f(x) =f(a)$$. In simple words, this implies that the value of the limit of the function will be equal to the value of the function at $$a$$ (i.e $$ f(a))$$, even when approaching from the left side of $$a$$ (i.e $$ x \to a^-$$) or from the right side of $$a$$ (i.e $$ x \to a^+$$) And the function is continuous on an interval ($$x_1,x_2)$$ if it's continuous at every point $$a$$, where $$a\in (x_1,x_2)$$.

Calculus

TutorMe

Question:

Evaluate the following indefinite integral as a power series, $$\int \frac{x^{2}}{1-x^{3}}\ {d}x $$.

Sudibyo G.

Answer:

Using the standard expression for Maclaurin series for $$ \frac{1}{1-x}= \sum_{n=0}^{\infty} x^n , \mid x \mid <1. $$ We can express $$ \frac{x^{2}}{1-x^{3}} = x^2.\frac{1}{1-x^3}=x^2\sum_{n=0}^{\infty} (x^3)^n= \sum_{n=0}^{\infty} x^{3n+2}$$. (Notice we replace $$x$$ with $$x^3$$ in the standard expansion) Thus, $$\int \frac{x^{2}}{1-x^{3}}\ {d}x = \int \sum_{n=0}^{\infty} x^{3n+2}\ {d}x = C+\sum_{n=0}^{\infty} \frac{x^{3n+3}}{3n+3} $$ for some constant $$C$$.

Send a message explaining your

needs and Sudibyo will reply soon.

needs and Sudibyo will reply soon.

Contact Sudibyo

Ready now? Request a lesson.

Start Session

FAQs

What is a lesson?

A lesson is virtual lesson space on our platform where you and a tutor can communicate.
You'll have the option to communicate using video/audio as well as text chat.
You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.

How do I begin a lesson?

If the tutor is currently online, you can click the "Start Session" button above.
If they are offline, you can always send them a message to schedule a lesson.

Who are TutorMe tutors?

Many of our tutors are current college students or recent graduates of top-tier universities
like MIT, Harvard and USC.
TutorMe has thousands of top-quality tutors available to work with you.