Processing math: 100%

Find the approximate value of f(3.02), where f(x) = 3x2+5x+3.

Solution :

Let y = f(x), x = 3 and x + δx. Then, δx.= 0.02.

For x = 3, we get

y = f(3) = 45

Now, y = f(x) y = 3x2+5x+3

dydx = 6x + 5   (dydx)x=3 = 23

Let δy be the change in y due to change δx in x. Then,

δy = dydx δx    δy = 23×0.02 = 0.46

f(3.02) = y + δy = 45 + 0.46 = 45.46


Similar Questions

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.

Verify Rolle’s theorem for the function f(x) = x2 – 5x + 6 on the interval [2, 3].

It is given that for the function f(x) = x36x2+ax+b on [1, 3], Rolles’s theorem holds with c = 2+13. Find the values of a and b, if f(1) = f(3) = 0.

Find the point on the curve y = cos x – 1, x [π2,3π2] at which tangent is parallel to the x-axis.

Leave a Comment

Your email address will not be published. Required fields are marked *