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TEA [102]
3 years ago
13

Consider the following equation. cos x = x3 (a) Prove that the equation has at least one real root. f(x) = cos x − x3 is continu

ous on the interval [0, 1], f(0) = 0, and f(1) = cos 1 − 1 ≈ −0.46 0. Since 0 −0.46, there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos x − x3 = , or cos x = x3, in the interval (0, 1). (b) Use your calculator to find an interval of length 0.01 that contains a root.

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
4 0

Answer:

b. 0.86, 0.87

Step-by-step explanation:

a. Find attached solution to a

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<em>Then</em><em>,</em><em> </em><em>compare</em><em> </em><em>2</em><em>3</em><em>.</em><em>0</em><em>4</em><em> </em><em>to</em><em> </em><em>2</em><em>2</em><em>.</em><em>3</em><em>2</em><em>.</em><em> </em>

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