Let f(x) = −x^4 − 4x^3.

(i) Find the intervals of increase/decrease of f.

(ii) Find the local extrema of f (values and locations).

(iii) Determine the intervals of concavity.

(iv) Find the location of the inflection points of f.

(v) Sketch the graph of f. (You can choose your own scale for the graph)

a) Given a vector field à = zỹ +(3y + 2)2 î in cartesian coordinates, determine whether it is solenoidal (V · À = 0), conservative (D x X = 0)

I Div x A (Cylinderical Coordinates)

ii) Calculate integral A*dl , where the contour C is the unit circle (r=1) traversed in anticlockwise direction

A uniform electric field is directed out of the page within a circular region of radius R = 2.50 cm. The magnitude of the electric field is given by E = (3.50 × 10-3 V/m•s)t, where t is in seconds. What is the magnitude of the magnetic field that is induced at radial distances (a)1.50 cm and (b)6.50 cm?

The rate of vocabulary memorization of the average student in a foreign language course is given by

=

where t is the number of continuous hours of study,

0 < t ≤ 4,

and v is the number of words. How many words would the student memorize in 3 hours? (Round your answer to the nearest whole number.)

words

You dive straight down into a pool of water. You hit the water with a speed of 5.0 m/s , and your mass is 70 kg.

Assuming a drag force of the form FDFD = (−1.50×10⁴ kg/s )v, how long does it take you to reach 2% of your original speed? (Ignore any effects of buoyancy.)

A white billiard ball with mass m_w = 1.33 kg is moving directly to the right with a speed of v = 2.96 m/s and collides elastically with a black billiard ball with the same mass m_b = 1.33 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of ?_w = 29

Based on the following companies in the U.S stock market .

(i) STI

(II) SBUX

(III) EBAY

(IV) BMO

(V) CM

(VI) FR

(VII) VMI

(VIII) SKX

(IX) HPQ

(X) VIOT

what are the following for each holding in the portfolio ?

(a) Each company profile

(b) Ticker

   (c) Name

   (d) key ratios

An undisturbed core of soil at field capacity was taken from a field site had a wet weight of 420 g. The following information was measured in the lab. The oven dry wt of the soil = 345 g Bulk Density = 1.15 g/cm3 What is the moisture content of the soil on a volume basis (volumetric water content Theta v)

A gas expands from point A to B. The expansion consists of two stages.

Stage 1) The gas expands at constant pressure from 15 to 39 litres.

Stage 2) The gas expands from 31 litres to 82 litres with a pressure drop according to the equation; P = 100 - 0.8 V kPa

Calculate the work done on the gas.