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)
∵ [tex]y=e^{x}[/tex]
- Differentiate it (remember the differentiation of [tex]e^{x}[/tex] is
∴ [tex]y'=e^{x}(1)[/tex]
∴ [tex]y'=e^{x}[/tex]
∵ dy = y' . dx
∴ [tex]dy=e^{x}dx[/tex]
∵ x = 0
∵ dx = Δx
∵ Δx = 0.6
∴ dx = 0.6
- Substitute x by 0 and dx by 0.6 in y'
∴ [tex]dy=e^{0}(0.6)[/tex]
- Remember any number to the power of 0 is 1 except 0
∵ [tex]e^{0}[/tex] = 1
∴ dy = 0.6
∵ Δy = f(x + Δx) - f(x)
∵ x = 0
- Substitute x by
∴ f(0) = [tex]e^{0}[/tex]
∴ f(0) = 1
∵ Δx = 0.6
∵ x + Δx = 0 + 0.6
∴ x + Δx = 0.6
- Substitute x by 0.6
∴ f(0.6) = [tex]e^{0.6}[/tex]
∴ 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
