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DedPeter
1 month ago
4

The function f is given by f(x)=0.1x4−0.5x3−3.3x2+7.7x−1.99. For how many positive values of b does limx→bf(x)=2 ?

Mathematics
1 answer:
lawyer [12.2K]1 month ago
5 0

Answer:

3

Stepwise explanation:

Begin by plotting the graph of the function

f(x)=0.1x^4-0.5x^3-3.3x^2+7.7x-1.99

and the graph of the line

y=2

This particular line crosses the function f(x) at four points. That means there are four distinct b values satisfying

\lim \limits_{x \to b} f(x)=2

Out of these, only three of those b values are positive.

For these positive values, since the line y=2 intersects f(x), we have f(x)=2. Therefore, for the three positive values of b,

\lim \limits_{x \to b} f(x)=2

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