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Last Minute Preparation to Finals

When Christmas trucks appear on silver screen letting us know that “Holidays are coming”, we hurry outside to play snowballs and buy gifts since the most cheerful and joyous time of the year has officially started and nothing can stop us. Nothing, except… finals. Acid looking students are rather poor show, however, exam tradition hasn’t been canceled yet, so we have to put up with it. Here we are to give some hints and don’t worry we won’t advise you that simple truth about time-management and stuff written in each every article within this topic.

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Chain Rule: Finding Derivatives Example

Taking a calculus class, you’ll surely be asked to find derivatives of functions. Sometimes it’s not that easy to do. If your function is not among common ones, you need to apply special rules to find its derivative: product rule, quotient rule, chain rule, etc. In this section we’re going to show you an example of using chain rule. Suppose we need to find the first derivative of the following function:

$h(x)=(2x^2+3)^{10}$

In fact, in this particular case, we can just open the braces using binomial theorem and obtain a polynomial, derivative of which is easily found due to table of derivatives. But not that fast, we have 10th power and opening the braces would be a troublesome business. So let’s try to use chain rule instead, you’ll appreciate simplification it suggests. (more…)

Jobs for Students – Earn while Learn!

You’re still at college but already worry about work experience? You are not alone seeking a good job with a possibility to balance it with studying. In figures, 1 in 7 students work full-time while study, 45% have part-time job, and almost 13% work both on weekends and week days. No matter what you are concerned with, be it money, self-affirmation or practice, work is a commonplace and integral part of students’ life, so let’s find out how to bring it together with your classes. (more…)

How to Find Derivatives Using Chain Rule?

If you’re asked to find a derivative of some function, sometimes it’s not a trivial thing to do. If you’re lucky and the function is among common functions, you can write down the required derivative right away using table of derivatives if necessary. But what if given expression is more complicated? That’s what this section is about. Let’s discuss chain rule for derivatives or so called outside-inside rule. This rule is needed when we want to find derivative of non-common function which is in fact composition of two or more common functions. (more…)

Why Do Coins Have Ribbed Edge?

Have a look at some change in your pocket and you’ll see that mostly coins have ribbed edges as if they are scarred. Such textured surface can be observed in almost every coin of the world no matter where it came from. Such coins appeared several centuries ago. So why are all of them ribbed?

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What Will Homework of Future Look Like?

Every day you can be surprised by homework facts: there’s always something new about devices which help us to do homework as well as about new cheating gadgets. Previously we’ve also told you everything about HW roots and history . And now, fancy, what a future of homework will be? What do you place your stake on? Will it be changed? Or will no longer exist? (more…)

Evaluate Improper Integrals with Beta Function

Earlier we’ve talked about gamma and beta functions.You’re probably interested, what beta function is useful for? In this section we’ll show how to integrate certain functions in simpler way with the help of beta function. Suppose we need to evaluate the following integral:

$\int_0^{3}{x^{1/2}(27-x^3)^{-1/2} dx}$

At first glance we can say that there is not an easy expression to deal with under the integral sign. As you can see we have radicals and powers under the integral sign so it’s not an easy thing to integrate directly. Moreover, take a look at the expression in braces: as it’s in negative power it means this is a denominator; and at the upper limit this denominator turns into zero. In other words, we’re facing an improper integral. And that’s what Euler’s functions are about! But which one should we take – gamma or beta? (more…)