Applying the limit concept, it is found that the limit is 2 for 3 positive values of b.
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The function given is:
[tex]f(x) = 0.1x^4 - 0.5x^3 - 3.3x^2 + 7.7x - 1.99[/tex]
The limit of the function as x tends to b is:
[tex]\lim_{x \rightarrow b} f(x) = 0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 1.99[/tex]
To find when the result of the limit is 2:
[tex]0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 1.99 = 2[/tex]
Placing into standard polynomial format:
[tex]0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 3.99 = 0[/tex]
Using a calculator, the solutions are: [tex]b_1 = -4.9978613719838, b_2 = 0.84536762603715, b_3 = 1.1540644992178, b_4 = 7.9984292467288[/tex]
Of those, 3 are positive, thus the limit is 2 for 3 positive values of b.
A similar problem is given at https://brainly.com/question/23625870
