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Find 100 consecutive natural numbers, each of which is composite

So this is the sort of quesition where you will spend a while thinking about it, probably feel a little silly you haven't gotten it yet, then go "aha!", write down the answer and move on. It's all ...
GV
Answered by Gabriel V. • STEP tutor
1871 Views

Evaluate the integral \int \frac{x}{x tan(x) + 1} dx using integration by substitution, hence evaluate \int \frac{x}{x cot(x) - 1} dx.

(STEP I 2017, Q1i)For the first part, the hint u = x sin(x) + cos(x) is given. It can be seen that this is the denominator once the fraction is multiplied by cos(x) / cos(x). The answer is ln(x sin(x) + cos(...
SV
Answered by Shreyas V. • STEP tutor
1131 Views

What do integrals and derivatives actually do/mean?

Integrals are frequently used in computing areas in two, three and even multidimensional space, thus they can be used to find out the "area" or "volume" of objects that we cannot even dra...
DF
1207 Views

Find h(x), for x≠0, x≠1, given that: h(x)+h(1/(1−x))=1−x−1/(1−x)

In order to do this question, we need to find some way of eliminating the h(1/(1−x)), so that we are left with h(x), thus solving it. One way to do this, is to set up simultaneous equations. We may need to s...
JO
Answered by Joss O. • STEP tutor
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Let p and q be different primes greater than 2. Prove that pq can be written as difference of two squares in exactly two different ways.

Without loss of generality claim p > q.Now, we try to write pq in the form pq = a 2 -b 2 where a and b are non-negative integers.If b = 0, then pq = a 2 . But p and q are different, so pq is not a square....
TL
Answered by Theodor L. • STEP tutor
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