Question

1) Derive the quotient rule

( f g ) ′ = (f ′ ⋅ g − f ⋅ g ′ )/g 2

using the product rule and the chain rule.

I was able to get this with product rule(i think) but unsure how to use chain rule

2) Identify a rate of accumulation (or decay) in your life that changes over time. Be creative.

a) Describe it in a sentence or two: the rate of accumulation of pages read this year

b) Sketch a plot of this rate as a function of time, be sure to label your axes: i read 2739 pages over 96 days

c) What does the area under this curve represent? I'm not sure what exactly the area means here but I think it is meaningless(what would the units be?)

3) Over a 200-day growing season a tree grows at a variable rate given by g ( t ) = 0.2 ⋅ sin ⁡ ( π t/ 200 ),

where t is time, in days and g(t) is the growth rate in kg/day. Use the Riemann sum approach to approximate the mass that this tree will put on over the course of the season, using five evenly sized bins.

I got approx 64.83 Kg

My points for the bins are (x,y), (40, 0.118), (80, 0.19), (120, 0.19), (160, 0.118), (200, 0)

4) Use geometric arguments to find the area under the piecewise function

f(x) = x, 0<x<=2

I got area 2 here just using 1/2 bh

f(x)=(4-(x-2)^2)^1/2 +2, 2<x<=6

I used A=w*h + 1/2 pi*r^2

my area is 6 + 2pi

HINT: try drawing the function first!

Answer 1

Please be informed that I m supposed to do first and only one question. So, it's my humble request please don't give negative rating because of that reason !!!