Enable contrast version

Tutor profile: Megan S.

Inactive
Megan S.
Tutor for six years
Tutor Satisfaction Guarantee

Questions

Subject: Calculus

TutorMe
Question:

Does the series from n=1 to infinity of n*(1/2)^n converge or diverge, and why?

Inactive
Megan S.
Answer:

Use the ratio test (plug in n+1 for n, multiply by the reciprocal of the original series, and take the limit of the absolute value of this as x approaches infinity). lim x-->inf (n+1)/2^(n+1) * 2^n/n Combine similar terms and simplify: lim x-->inf (2^n)/(2^(n+1)) * (n+1)/n lim x-->inf (1/2)*(n+1)/n = 1/2 Since the limit equals 1/2, which is less than 1, the series converges by the ratio test.

Subject: Calculus

TutorMe
Question:

Find the derivative of f(x) = 5/(e^4x + x^3).

Inactive
Megan S.
Answer:

First, since there are no variables in the numerator, we can rewrite the function as f(x) = 5(e^4x + x^3)^(-1). Now we can use the chain rule instead of the quotient rule. For the chain rule, multiply by the exponent, subtract one from the exponent, and then multiply by the derivative of the inside: f'(x) = -5*(e^4x + x^3)^(-2)*(4e^4x + 3x^2). We can rewrite this as f'(x) = -5(4e^4x + 3x^2) / (e^x + x^3)^2.

Subject: Algebra

TutorMe
Question:

Write the following expression as a single logarithm: 2log(x) - 3log(y) + (1/2)log(z)

Inactive
Megan S.
Answer:

First, write the coefficients as exponents (1/2 power is the square root): log(x^2) - log(y^3) + log(sqrt(z)) Now we can combine the terms into a single log (add-->multiply, subtract-->divide): log(x^2*sqrt(z) / y^3)

Contact tutor

Send a message explaining your
needs and Megan will reply soon.
Contact Megan

Request lesson

Ready now? Request a lesson.
Start Lesson

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 Lesson" 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.