i have no idea how to start it at all?

Question

i am stuck at the last 2 problems of my homework, and it dues tomorrow. hopefully someone can help me asap. thanks.

1. find Δy and Δy/Δx, given
a) y=2x-3 and x changes from 3.3 to 3.5
b) y=x²+4x and x changes from 0.7 to .85
c) y=2/x and x changes from .75 to .5

2. find Δy, given y=x²-3x+5, x=5, and Δx=-.01.
what then is the value of y when x=4.99?

Answer 1

Δx is the difference in x values (Δ, the Greek letter delta, means "change of"). So if x goes from 3.3 to 3.5, Δx = 0.2. To find Δy, plug in x=3.3 and x=3.5 to get two y values, then take the second value minus the first value. This tells you how much y changes when x changes. Then Δy/Δx is just a matter of dividing one by the other.

Answer 2

a) (2(3.5) - 3) - (2(3.3) - 3) = .4 = Δy
3.5 - 3.3 = .2 = Δx
so, Δy/Δx = .4 / .2 = 2

b) (.85^2 + 4(.85)) - (.7^2 + 4(.7)) - = .8325 = Δy
.85 - .7 = .15 = Δx
so, Δy/Δx = .8325 / .15 = 5.55

c) 2 / .5 - 2 / .75 = 1.33 = Δy
.5 - .85 = -.35 = Δx
so, Δy/Δx = .1.33 / -.35 = -3.8

2. when x = 5, y = 5^2 -3(5) + 5 = 15
when x = 4.99, y = 4.99^2 -3(4.99) + 5 = 14.93,
so Δy = 15 - 14.93 = .07

Answer 3

OK give you an example:
y = 2x - 3
If x = 3.3, y = 2(3.3) - 3
so y = 3.6

if x = 3.5, y = 2(3.5) - 3
so y = 4

Now Δy = 4 - 3.6 = 0.4
and Δy/Δx = 0.4/(3.5 - 3.3)
= 0.4/0.2 = 2

You can do the rest

2. y=x²-3x+5, x=5, and Δx=-.01
When x = 5, y = 25-15+5 = 15
When Δx=-0.01 that means now x = 5-0.01 = 4.99
y = 4.99^2 -3(4.99)+5 = 14.9301

So, Δy = 15 - 14.9301 = -0.0699

Answer 4

You do all three of the first group the same way. Take (a)
y = 2*3.3 - 3 = 3.6
y = 2*3.5 - 3 = 4
Δy = 4 - 3.6 = .4
Δx = 3.5 - 3.3 = .2
Δy/Δx = .4 / .2 = 2

The 2'nd one is basically the same. Evaluate it at 5 and at 5 - .01 (4.99)

HTH

Doug

Answer 5

y(3.3)=2(3.3)-3
y(3.5)=2(3.5)-3
dy = .4 d for delta
y(.85)=(.85)^2 + 4(.85)
y(.7)=(.7)^2 +4(.7)
dy=.2325+.6=.8325
y(.75)=2/.75
y(.5)=2/.5
dy=y(.75)-y(.5)=4/3

don't understand other problem.