I am a DSP Engineer and a mathematician working in closely related areas of DSP, Digital Control, Digital Comm and Error Control Coding. I have a passion for both Pure and Applied Mathematics.

November 27, 2018 – 10:40 pm
Time is Life.

Money lost can come back, but time lost can never come back. Time is more valuable than money. (Bertrand Russell).

November 27, 2018 – 10:36 pm
The object of pure Physics is the unfolding of the laws of the intelligible world; the object of pure Mathematic that of unfolding the laws of human intelligence. — J. J. Sylvester.

*In my opinion, for example, Boole’s Laws of (Human) Thought. *

November 27, 2018 – 10:07 pm
Newton’s patience was limitless. Truth, he said much later, was the offspring of silence and meditation. And, he said, I keep the subject constantly before me and wait till the first dawnings open slowly, by little and little into a full and clear light.

November 13, 2018 – 3:16 pm
**Question I:**

Show that the equation of the tangent to the curve and can be represented in the form:

**Question 2:**

Show that the derivative of the function , when and , when vanishes on an infinite set of points of the interval $latex (0,1), Hint: Use Rolle’s theorem.

**Question 3:**

Prove that for . Use Lagrange’s theorem.

**Question 4:**

Find the largest term in the sequence . Hint: Consider the function in the interval .

**Question 5:**

A point P is given on the circumference of a circle with radius r. Chords QR are drawn parallel to the tangent at P. Determine the maximum possible area of the triangle PQR.

**Question 6:**

Find the polynomial of degree 6, which satisfies and has a local maximum at and local minimum at and 2.

**Question 7:**

For the circle , find the value of r for which the area enclosed by the tangents drawn from the point to the circle and the chord of contact is maximum.

**Question 8:**

Suppose that f has a continuous derivative for all values of x and , with for all x. Prove that .

**Question 9:**

Show that , if .

**Question 10:**

Let . Show that the equations has a unique root in the interval and identify it.