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Katie F.

Calculus I, II and III tutor for four years at the University of San Diego

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Java Programming

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Question:

Write a class in java to run the main method that will display "Hello world" every time the user types "Go."

Katie F.

Answer:

public class HelloWorld{ public static void main(String[] args) { Scanner reader = new Scanner(System.in); String input = reader.nextLine(); if (input.equals("Go") || input.equals("go")) { System.out.println("Hello world"); } } }

Calculus

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Question:

What is lim x-> 0 [sin(x) / x], read as "the limit as x approaches zero of sin of x all over x?"

Katie F.

Answer:

We note that if we plug in x = 0 to sin(x) / x, we get 0 / 0, allowing us to use L'Hospital's rule. Following this rule, we can take the derivative of the numerator and denominator separately (note: you do not need to use the quotient rule). We end up with lim x-> 0 [cos(x) / 1]. When plugging in x = 0, we get 1 as the answer.

Algebra

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Question:

You and your best friend are trying to create matching posters for your bedroom walls on the computer. Each of you is making your own poster on your own computer. You want them to be exactly the same size. Your best friend's poster has a width of 20 inches, but she can't figure out how tall it is. Your poster is the exact same photo but is 15 inches wide and 30 inches tall. How much do you need to increase the height of your poster so that it's exactly the same size as your best friend's?

Katie F.

Answer:

This is a two step question: 1. Find out how tall your best friend's poster is. 2. Find the difference between the height of her poster and the height of yours. Solution: 1. Figure out the right proportions width of friends/width of yours = height of friends/height of yours Therefore, 20/15 = x/30 20*30 = 15*x x = 600/15 x = 40 So now your know your friend's poster is 40 inches tall. 2. If your poster is 30 inches tall and hers is 40 inches tall, then you have to increase the size of your poster by 40-30 = 10 inches

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