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A curve has the equation (5-4x)/(1+x)

Start by looking for intercepts.x=0, y= 5. Therefore the curve crosses the y axis at y=5y=0, x= 5/4these are the only two intercepts. Now look for asymptotes.3. at x= 1, y becomes undefined, looking at eithe...
HH
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Evaluate the following product of two complex numbers: (3+4i)*(2-5i)

Answer : 26-7iMethod : Expanding the brackets will result in the sum, 6 -15i + 8i - 20i 2 by assessing this you can see that you can evaluate -15i + 8i to be equal to -7i which is the imaginary part of the c...
CB
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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
2269 Views

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...
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