Question

Use the information to evaluate and compare ∆y and dy?

y = x^4 + 1, x = -5, dx = 0.01
A) ∆y = 0.01, dy = 1024.01
B) ∆y = 0.01, dy = 0.01
C) ∆y = 1024.01, dy = 0.01
D) ∆y = 1024, dy = 1024.

Answer 1

To evaluate ∆y and dy, substitute the given values into the equation and perform the calculations. The correct answer is D) ∆y = 1024, dy = 1024.

Step-by-step explanation:

The given equations are:

y = x^4 + 1

x = -5

dx = 0.01

To evaluate ∆y and dy, we need to substitute the given values into the equation.

∆y = (x+dx)^4 + 1 - (x^4 + 1)

∆y = (-5+0.01)^4 + 1 - (-5^4 + 1)

∆y = 0.01^4 - 5^4

∆y ≈ 0.00000001 - 625

∆y ≈ -624.99999999

dy = y(x+dx) - y(x)

dy = (-5+0.01)^4 + 1 - (-5)^4 + 1)

dy = 0.01^4 - (-5)^4

dy ≈ 0.00000001 - 625

dy ≈ -624.99999999

Therefore, the correct answer is D) ∆y = 1024, dy = 1024.