TutorMe homepage

SIGN IN

Start Free Trial

Nikhil B.

Tutor for 4 years now

Tutor Satisfaction Guarantee

Organic Chemistry

TutorMe

Question:

What are the Isomers of Pentane?

Nikhil B.

Answer:

Pentane (C5H12) has three structural isomers. Isomer 1 is n-pentane, the straight chain normal structure for pentane Isomer 2 is 2-methylbutane, a branched chain with a carbon* atom joined onto three other carbon atoms. Isomer 3 is 2,2-dimethylpropane, a branched chain with the central carbon* atom joined onto four other carbon atoms. Note that for all the isomers, each carbon atom has four bonds (valency 4), and each hydrogen atom has one bond (valency 1). Valency is the combining power of an atom. You cannot change the number of bonds that each atom has.

Calculus

TutorMe

Question:

How do you evaluate the integral ∫ x^4/(1+x^2) dx ?

Nikhil B.

Answer:

x*4/(x*2+1) = (x^2-1) + 1/1+x^2 So, integrating both sides , we get x^3/3 - x + ∫dx/1+x^2 now let x = tanθ , dx = sec^2θdθ and x^2 + 1 = 1 + tan^2θ = sec^2θ therefore, ∫dx/1+x^2 = ∫dθ = θ = arctan(x) putting it all together ∫x*4/(x*2+1) = x^3/3 - x +arctan(x) + C

Algebra

TutorMe

Question:

Find the roots of f(x) = 2x3 + 3x2 – 11x – 6 = 0, given that it has at least one integer root.

Nikhil B.

Answer:

ince the constant in the given equation is a 6, we know that the integer root must be a factor of 6. The possible values are Step 1: Use the factor theorem to test the possible values by trial and error. f(1) = 2 + 3 – 11 – 6 ≠ 0 f(–1) = –2 + 3 + 11 – 6 ≠ 0 f(2) = 16 + 12 – 22 – 6 = 0 We find that the integer root is 2. Step 2: Find the other roots either by inspection or by synthetic division. 2x3 + 3x2 – 11x – 6 = (x – 2)(ax2 + bx + c) = (x – 2)(2x2 + bx + 3) = (x – 2)(2x2 + 7x + 3) = (x – 2)(2x + 1)(x +3) So, the roots are x=2,-0.5,-3

Send a message explaining your

needs and Nikhil will reply soon.

needs and Nikhil will reply soon.

Contact Nikhil

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.

Made in California

© 2019 TutorMe.com, Inc.