**Unformatted text preview: **Figure 6.18 y = tan x and y = 2 x . Exercises 1. Approximate the ﬁfth root of 7, using x = 1 . 5 as a ﬁrst guess. Use Newton’s method to ﬁnd x 3 as your approximation. ⇒ 2. Use Newton’s Method to approximate the cube root of 10 to two decimal places. ⇒ 3. The function f ( x ) = x 3-3 x 2-3 x + 6 has a root between 3 and 4, because f (3) =-3 and f (4) = 10. Approximate the root to two decimal places. ⇒ 4. A rectangular piece of cardboard of dimensions 8 × 17 is used to make an open-top box by cutting out a small square of side x from each corner and bending up the sides. (See exercise 6.1 . 20 .) If x = 2, then the volume of the box is 2 · 4 · 13 = 104. Use Newton’s method to ﬁnd a value of x for which the box has volume 100, accurate to 3 signiﬁcant ﬁgures. ⇒...

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- Fall '07
- JonathanRogawski
- Math, Calculus, Numerical Analysis, Approximation, Derivative, ........., Decimal