Let f(x)=\sqrt{100 - x^2}. Use differentials (linear approximation) to estimate f(8.2). Base your approximatio

Answer 1

y = (100 - x^2)^(1/2)
y^2 = 100 - x^2
2ydy = -2xdx
y(8) = 6
6(y - 6) ≈ -8(x - 8)
6y - 36 ≈ 64 - 8x
y ≈ (100 - 8x)/6
y(8.2) ≈ (100 - 8*8.2)/6
y(8.2) ≈ 5.733333

y(8.2) = 5.723635

Answer 2

all of us understand that dy=f'(x)dx, and we are able to calculate f(6)=8. Differentiating the equation: f'(x)=(one million/2) [(a hundred-x^2)^(-one million/2)] (-2x) Simplifying: -x [(a hundred-x^2)^(-one million/2)] Plugging in x=6 we get. -6[a hundred-36]^(-one million/2)] = -6(one million/8) =-3/4 all of us understand dx=.2, multiplying, we get: dy=(-0.75)*(.2)=-0.15 upload the cost of f(6) to get: f(6.2)?7.80 5