Enable contrast version

# Tutor profile: Rachael A.

Inactive
Rachael A.
Tutor Satisfaction Guarantee

## Questions

### Subject:Set Theory

TutorMe
Question:

Let $$R = \{a,b,c \}, S = \{ a,b,d \}, T = \{ e,f \}$$. List the elements in the set $$(R \cup S) \cap (R \cup T)$$.

Inactive
Rachael A.

SETUP: If we are asked to find the set $$(R \cap S) \cup (R \cap T)$$, this means we are asked to find the union of the set $$(R \cap S)$$ with the set $$(R \cap T)$$. In order to do this, I first need to find the elements of the sets $$(R \cap S)$$ and $$(R \cap T)$$. That means that step one is to find the set $$(R \cap S)$$, step two is to find the set $$(R \cap T)$$, and step three is to find the union. STEP ONE: Find $$(R \cap S)$$. By definition of intersection, the elements of $$(R \cap S)$$ are all the elements that appearing in both $$R$$ and $$S$$. I start by looking at the elements in $$R$$ and check to see if they are also in $$S$$. The element $$a$$ appears in $$R$$ and also in $$S$$, the element $$b$$ appears in $$R$$ and also in $$S$$, but the element $$c$$ appearing in $$R$$ does not appear in $$S$$. Therefore the only elements appearing in both $$R$$ and $$S$$ are $$a$$ and $$b$$. This means $$(R \cap S) = \{ a, b\}$$. STEP TWO: Find $$(R \cap T)$$. By definition of intersection, the elements of $$(R \cap T)$$ are those appearing in both $$R$$ and $$T$$. There are no elements in $$R$$ that appear in $$T$$ so this set is empty. In other words, $$(R \cap T) = \emptyset$$. STEP THREE: Find $$(R \cap S) \cup (R \cap T)$$. It is easiest to start by listing the elements of $$(R \cap S)$$ and $$(R \cap T)$$ next to each other, so we can use this to compare. We can do this because of the work we did in steps one and two. $$(R \cap S) = \{ a, b\}$$. $$(R \cap T) = \emptyset$$. We are asked to find the union of these two sets. By definition of union, the elements in this set are all the elements that appear in either $$(R \cap S)$$ or $$(R \cap T)$$. Since $$a$$ and $$b$$ are in $$(R \cap S)$$, they will be elements in our set. We next add in all the elements of $$(R \cap T)$$. Since $$(R \cap T)$$ is empty, there are no more elements that will be in our set. Therefore $$(R \cap S) \cup (R \cap T) = \{ a, b\}$$.

### Subject:Discrete Math

TutorMe
Question:

An urn contains balls numbered 1 through 9. Suppose that you draw a ball from the urn, observe its number, do notreplace the ball, draw again. You repeat this until you have drawn a ball four times. What's the number of possible ways you can have performed this task?

Inactive
Rachael A.

There are four actions: to draw the first ball, to draw the second ball, to draw the third ball, to draw the fourth ball. On the first draw, there are still 9 options. However, on the second draw, because you kept your first ball, you only have 8 balls left in the urn to choose from, so there are only 8 options. The same thing holds for the next two draws, in that there is one less ball to choose from. Therefore the total number of possible outcomes is $$9 \cdot 8 \cdot 7 \cdot 6$$.

### Subject:Calculus

TutorMe
Question:

Use the comparison test to determine whether the following integral diverges or converges: $$\int_{0}^1 ln(x^{1/x})dx$$

Inactive
Rachael A.

The integral diverges. Note first that $$\int_{0}^1 ln(x^{1/x})dx = \int_{0}^1 \frac{ln(x)}{x} dx \leq \int_0^1 ln(x)dx$$ since a negative value times a number larger than 1 is a larger negative value. But \begin{align*} \int_0^1 ln(x)dx &= \lim_{t \rightarrow 0} x ln(x) - x |_{t}^1 \\ &= 0 ln(1) - 1 - \lim_{t \rightarrow 0} t ln(t) - t \\ &= -1 - \lim_{t \rightarrow 0} \frac{ln(t)}{t^{-1}} - 0 \\ &= -1 - \lim_{t \rightarrow 0} \frac{1/t}{-t^{-2}} = - \infty \end{align*} by L'Hospital's rule.

## Contact tutor

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

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.
BEST IN CLASS SINCE 2015
TutorMe homepage