Tutor profile: Breanna P.

What should I include in my introduction of an essay?

The principal purpose of an introduction in anything is to give the audience an understanding of what the following pages will bring, while simultaneously grabbing their attention. Start broadly with a hook and then, in the following couple sentences, narrow the reader's attention down to the specifics your paper will hold. I like to write a hook that includes the "umbrella" of the topic, followed by anywhere from one to three sentences about what the essay will be about. There is no reason that an introduction in a standard essay (thinking typical five paragraphs) needs to be long or overly wordy. Grab your audience's attention and get to the point.

Solve the following and give your solution as a mixed number. -3 * -12/7

To begin, let's look at the signs. When you multiply two negative numbers, the answer will be a positive number. Since we are dealing with fractions, it might be easier to imagine that the number 3 is a fraction as well. -3 = -3/1. Now, let's multiply numerators (tops) and denominators (bottoms) straight across. This gets us (3*12)/(1*7) = 36/7. To make this a mixed number, think about how many times 7 can fully go into 36. It can go into it 5 times to reach 35, and it would leave 1. So the mixed number, and the answer to this problem, is 5 and 1/7.

How do I find the antiderivative of ln x?

The best way to solve this question would be to take the integral of ln x. Integration by parts is the optimal method to use. The formula for this is the integral of u * dv = u*v - the integral of v * du. Start with your function, the integral of ln x * dx. To evaluate, set parameters u = ln x and dv = dx. This would yield du = 1/x * dx [taking the derivative of ln x) and v = x [the integral of dx]. Using integration by parts, you would plug in these values to arrive at the answer: x * ln x - x + C.