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wel
2 years ago
14

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 − 2x, (0

, 1) The equation ex = 3 − 2x is equivalent to the equation f(x) = ex − 3 + 2x = 0. f(x) is continuous on the interval [0, 1], f(0) = _____, and f(1) = _____. Since f(0) < 0 < f(1) , 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 ex = 3 − 2x, in the interval (0, 1)
Mathematics
1 answer:
raketka [301]2 years ago
3 0

Answer:

f(0)=-2\\f(1)=e-1

Step-by-step explanation:

According to intermediate value theorem, if a function is continuous on an interval [a,b], and if k is any number between f(a) and f(b), then there exists a  value, x=m, where a, such that f(m)=k

In the given question,

Intermediate Value Theorem is used to show that there is a root of the given equation in the specified interval.

Here,

f(x)=e^x-3+2x

Put x=0

f(0)=e^0-3+2(0)=1-3+0=-2

Put x=1

f(1)=e^1-3+2(1)=e-3+2=e-1

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