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Let's run through an example: proving by induction that n^2 = 1 + 3 + ... + (2n-1) for all integers n>0. Remember that when asked to use induction to prove a statement, you first need to show that the ...

The tangent to the curve is a straight line and will hence have the form f(x) = m * x + c, where m is the gradient of the tangent line and c is the y-intercept of the tangent line.
The gradient of th...

If you are comfortable with differentiation. You can take the second derviatve of the equation of the cruve and plug in the x value of the curve. Based on this answer you can determine if it's a maximum, ...

Given: A = [a -5; 2 a+4]. 1) First find the determinant of A using the known formula => det A = a²+ 4a + 10. A singular matrix is ...

First of all calculate the complex conjugate of the denominator. The complex conjugate of (1-i) is 1+i.Now multiply the given complex number by (1+i)/(1+i), note that we are not modifying the starting num...