Question

If y = x^2 and x change from x0 = 8 to x1=12 , find : A) delta x B) delta y C) dy D)Approximate the relative error in y Could somebody help me to solve this problem please ? Any help would be greatly appreciated !

Answer 1

Please see the Explanation.

Explanation:

Given that, `y=x^2.`

`x` changes from `x_0=8` to `x_1=12`.

`:. y_0=x_0^2=8^2=64, and, y_1^2=x_1^2=12^2=144`.

(A) : `:. deltax"=(change in "x)=x_1-x_0=12-8=4`.

(B) : `deltay"=(change in "y)=y_1-y_0=144-64=80`.

(C) : `dy=d(x^2)=d/dx(x^2)dx, or, (x^2)'dx=2xdx.`

(D) : `"The Relative Error in "y=(deltay)/y`.

But, `deltay~~dy/dx*deltax rArr (deltay)/y~~1/y*dy/dxdeltax`.

`:.", for "y=x^2, "the Relative Error in "y~~1/x^2*2xdeltax=2(deltax)/x`.

Note that, since `(deltax)/x` is relative error in `x`,

for `y=x^2," the Relative Error in "y~~2xx"that in "x`.