Saniya K.

Masters in Mathematics and Statistics Student

Tutor Satisfaction Guarantee

SAT

TutorMe

Question:

I love SAT Math and it was my favorite section on the SATs. I hope I can help you with the concepts.

Saniya K.

Answer:

Please ask me any math question! I got a good score in my SAT Math Exam, well-above the 700s.

GRE

TutorMe

Question:

x^2 + 1 versus 2x - 1. How do we know which is greater?

Saniya K.

Answer:

Please note that x^2 + 1 is a quadratic term that will always be greater. f(x) = x^2 + 1 g(x) = 2x - 1 The 3 cases that we evaluate are x < 0, x = 0, and x > 0. These collectively represent all possibilities for x. For x < 0 then 2x - 1 yields negative values. However, x^2 + 1 has x^2, which is always positive and therefore x^2 + 1 is always positive. Therefore, for x < 0, x^2 + 1 > 2x - 1. Next, when x = 0, then f(x) = x^2 + 1 --> f(0) = (0)(0) + 1 = 1. Thus, x^2 + 1 --> 1. Here, g(x) = 2x - 1 --> g(0) = (2)(0) - 1 = 0 - 1 = -1. Thus, 2x - 1 = -1 when x = 0. Therefore, for x = 0, x^2 + 1 > 2x - 1. Finally, for x > 0, we can look and see that for instance, for x = 1, f(1) = (1)(1) + 1 = 2 and g(1) = (2)(1) -1 = 2 - 1 = 1 so x^2 + 1 > 2x - 1. In fact, the parabolic f(x) = x^2 + 1 will be everywhere above the straight line g(x) = 2x - 1. Here f(x) is growing at the rate: f'(x) = d/dx [x^2 + 1] = 2x + 0 = 2x, which goes up exponentially. On the other hand, g(x) is going up with the slope of 2 so g'(x) = 2. Then, 2x > 2 growth for x > 1. Between 0 < x < 1, f(x) is above g(x) anyways and g(x) = 0 for x = 0.5, while f(x) is always above 0. Therefore, please note that in general for all 3 cases, f(x) = x^2 + 1 is always above g(x) = 2x - 1. Please note the behavior of each of these functions by looking at these lines: f(x) : https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=x%5E2%20%2B%201 g(x) : https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=y+%3D+2x+-+1

Calculus

TutorMe

Question:

What are some of the indeterminate forms that L'Hospital's Rule would help us find the derivative of?

Saniya K.

Answer:

These indeterminate forms, for which L'Hospital's Rule is helpful if if we are finding the limit of f(x) / g(x) where evaluating the limits lead to: (∞/∞, -∞, ∞, 0/0). Other indeterminate forms are like: 1^∞, 0^0, ∞^0, ∞-∞. Here, there is no conceptual way or defined way to evaluate these forms and thus we please have to find the derivatives of f(x) and g(x) and then evaluate the limit of the derivatives: limit of f'(x) / g'(x) and that will be equivalent here.

Send a message explaining your

needs and Saniya will reply soon.

needs and Saniya will reply soon.

Contact Saniya

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.