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PART A Question 1 1. Differentiate the following functions...

PART A Question 1 1. Differentiate the following functions: (a) ((x)=-4x2 = + 3x - 1 (c) h(x) = 3e* 'vx' + 1 [30 marks) 2. For function f(x) in 1a, write down the difference ratio at (equivalently indicated with or, and show that the limit for the increment going to zero is equal to the de...

INSTRUCTIONS: Do all of the following 6 problems. N.B. Show...

INSTRUCTIONS: Do all of the following 6 problems. N.B. Show an adequate amount of work and justiÖcation for your answers. 1. The equation of motion of the projectile thrust vertically from the surface of the earth, when air resistance is taken into account, but changing of gravitational force...

7. A taut string with constant linear density p has its end...

7. A taut string with constant linear density p has its ends at x = 0 and x = 8 on the x-axis. The tension in the string is a constant T. The end x = 0 is free to slide without friction along a vertical support and the end x = 8 is held a fixed distance y = 3 above the x-axis. A damping force pro...

4. Consider the differential equation (x2 + 1) y" ...

4. Consider the differential equation (x2 + 1) y" + 4xy = 0. 80 (a) Without solving, if y(x) = an xn is used to solve this differential equation, is it possible to predict (with 100% certainty) that the n=0 solution will be a general solution? If yes, find the open interval of converg...

Give an example of a connected undirected graph that contain...

Give an example of a connected undirected graph that contains at least twelve vertices that contains at least two circuits. Draw that graph labeling the vertices with letters of the alphabet. Determine one spanning tree of that graph and draw it. Determine whether the graph has an Euler circ...

4. Use the Laplace Transform method to solve the following d...

4. Use the Laplace Transform method to solve the following differential equation problem: y′′(t) + y(t) = e−³ ͭ , y(0) = 1, y′(0) = 0. 5. Use the z-transform method to solve the following difference equation: y[n + 2] = y[n + 1] + 6y[n], y[0] = 0, y[1] = 1.

Homework 4 Q1. [30pt For each statement below, indicate whe...

Homework 4 Q1. [30pt For each statement below, indicate whether the statement is true or false If it is true, provide proof, otherwise, provide counterexample. [Each part is 5pt.] a. Let X [a,bland be metric defined on X. Let / a,6] -> [a,b] be continuous function such that f(x)< f...

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