(a)
well, we have a point and a slope (5), so
y-8 = 5(x+1)
(b)
dy = 10/(x^2+1) dx, so if dx=1,
dy = 10/2 (1) = 5
So, the estimate is 8+5 = 13
(c)
F(0)-F(-1) = 7.854
F(0) = 7.854 + F(-1) = 7.854+8 = 15.854
I hope that (c) had a typo and didn't want f(0), since f(0) = 10. (f(x) = dy/dx)
Let f be the function that contains the point (-1,8) and satisfies the differential equation dy/dx=10/(x^2+1)
(a) Write the equation of the tangent to f at x=-1.
(b) Use your equation in part a to estimate f(0).
(c) We know that the integral from -1 to 0 of 10/(x^2+1) equals about 7.854 and the integral from a to b of f(x)dx = F(b)-F(a). Use this to find f(0).
I think i did parts a and b right. i got y-8=5(x+1) for part a and f(0)=13 for part b, but i don't know how to do part c at all.
Thank you!
3 answers
it wasn't a typo.. how did you get 10?
well, they told us that f(x) = 10/(x^2+1)
Looks to me like f(0) = 10/(0+1) = 10
Looks to me like f(0) = 10/(0+1) = 10
1 answer