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Could you explain to me how proof by induction works?

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 sta...
JB
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Find the equation of the tangent to the curve y = exp(x) at the point ( a, exp(a) ). Deduce the equation of the tangent to the curve which passes through the point (0,1) .

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 the tangen...
CT
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How do I determine if a stationary point on a curve is the maximum or minimum?

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, min...
ES
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Show that the matrix A is non-singular for all real values of a

Given: A = [a -5; 2 a+4] . 1) First find the determinant of A using the known formula => det A = a 2 + 4a + 10 . A singular matrix is one in which it's determinant equals zero (the determinant of a matrix...
9632 Views

Express the complex number (1+i)/(1-i) in the form x+iy

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 number...
CM
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