Question

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

Answer 1

Answer:

Δy = 0.822

dy = 0.6

Step-by-step explanation:

Let us use the rules:

If f(x) = y, then

• dy = f'(x) . dx
• Δy = f(x + Δx) - f(x)

∵ $y=e^{x}$

- Differentiate it (remember the differentiation of $e^{x}$ is

∴  $y'=e^{x}(1)$

∴  $y'=e^{x}$

∵ dy = y' . dx

∴ $dy=e^{x}dx$

∵ x = 0

∵ dx = Δx

∵ Δx = 0.6

∴ dx = 0.6

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

∴ $dy=e^{0}(0.6)$

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

∵ $e^{0}$ = 1

∴ dy = 0.6

∵ Δy = f(x + Δx) - f(x)

∵ x = 0

- Substitute x by

∴ f(0) = $e^{0}$

∴ f(0) = 1

∵ Δx = 0.6

∵ x + Δx = 0 + 0.6

∴ x + Δx = 0.6

- Substitute x by 0.6

∴ f(0.6) = $e^{0.6}$

∴ 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