Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.)
y = ex, x = 0, Δx = 0.6

Δy = 0.822

dy = 0.6

Step-by-step explanation:

Let us use the rules:

If f(x) = y, then

∵

- Differentiate it (remember the differentiation of is

∴  

∴  

∵ dy = y' . dx

∴

∵ x = 0

∵ dx = Δx

∵ Δx = 0.6

∴ dx = 0.6

- Substitute x by 0 and dx by 0.6 in y'

∴

- Remember any number to the power of 0 is 1 except 0

∵ = 1

∴ dy = 0.6

∵ Δy = f(x + Δx) - f(x)

∵ x = 0

- Substitute x by

∴ f(0) =

∴ f(0) = 1

∵ Δx = 0.6

∵ x + Δx = 0 + 0.6

∴ x + Δx = 0.6

- Substitute x by 0.6

∴ f(0.6) =

∴ f(0.6) = 1.8221188

∵ Δy = f(0.6) - f(0)

∴ Δy = 1.8221188 - 1

∴ Δy = 0.8221188

- Round it to the nearest 3 decimal places

∴ Δy = 0.822

answer: h=5.6 i don't really know how to put into words, so i though i would let you do that. i hope i was able to some

step-by-step explanation:

18 = 6(h)+1/2

18 = 6h+1/2

18-1 = 6h/2

17 = 3h

17/3 = h

h = 5.6