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First of all, multiply secx by (secx+tanx)/(secx+tanx). Use the substitution u=secx+tanx, so that du=(secxtanx+sec²x) dx and then substitute both terms. Calculate the integral of the du/u arriv...

This qustion can be solved easily using the gradient formular, m = ∆y/∆x, and some simple algrebra.

The gradient at the point x = 2 is calculated by find the gradient of a tangent at x = 2. To find...

We can expand following any row or column we want. A wise choice would be to use a row/column in which we have one or more zero entries to reduce the calculations. From this, we pick the first entry on th...

1/z =1/(4+i) Multiply both top and bottom by the complex conjugate, z* = 4 - i, 1/z = (4-i)/((4+i)(4-i)) = (4-i)/(16+4i-4i-i²) = (4-i)/17 ans: 4/17 - i/17

Let P(n) be the statement “(n^3)-n is divisible by 3”

First we’ll examine the base case: P(1)

(n^3)-n=1^3-1=1-1=0

0=3*0, so is divisible by 3, and so P(1) is true

Now assume fo...