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Define Dot Product its formula and its physical interpretation.
A man drives from Detroit to Chicago, say 300 mi., at an average speed of 60 mi. per hr., stops
1 hr. in Chicago, and returns at a speed of 50 mi. per hour. Neglecting variations of speed en-route:
Write formulas expressing x (distance from Detroit) as a function of t.
If F(t) = 4t^2i - tj + t^2k and G(t) = ti + 2t^2j + 4 sin t k, then find (cos t F)
If F(t) = 4t^2i - tj + t^2k and G(t) = ti + 2t^2j + 4 sin t k, then find d/dt (F*G)
An object in free fall from
50 m high, so the height is
when t is h(t) = 50 – 4.9t2
.
What is the speed at
t = 2?
2. Determine the equation of the tangent line
on the curve y = x3 at the point (2.8)
An object in free fall from
50 m high, so the height is
when t is h(t) = 50 – 4.9t2
.
What is the speed at
t = 2?
2. Determine the equation of the tangent line
on the curve y = x3 at the point (2.8)
f'(x) of f(x) = 2x^2 + 8x = 10
Q.1: Apply Gauss's Divergence theorem to evaluate double integration S (lx^ 2 +my^ 2 +nz^ 2 )dS taken over the sphere (x-a)^ 2 +(y-b)^ 2 +(z-c)^ 2 = rho^ 2 ;l,m,n being the direction cosines of the external normal to the sphere.
Micros Unlimited corporation (a local distributor of micro computers) sells one of its 586-based system on a volume
discount as follows: 1 to 5 units at a price of $4495 per unit, units 6 through 10 at a price of $ 4095 per unit, and
any unit in excess of 10 at a price of $3775 per unit.
i. Determine the cost function and draw its graph.
ii. What are the total and average cost s of 4 units ?
iii. What are the total and average cost s of 15 units?
iv. How many units were purchased if the total charge was $58,050 ?
v. How many units were purchased if the average charge was $4035?
Find the minimum distance from the point (4, 2) to the parabola y²=8x.
