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I have come across two questions that I have solved, but unfortunately am quite sure I've done them incorrectly. They are related to continuity and the intermediate value theorem.

Find the constant c that makes g continuous (-infinity,infinity).

g(x){ x^2-c^2 if x<4

{ cx+20 if x>4

For this question I found that the graphs is continuous from (-infinity,4),[4,infinity] Then I found the limits as x approaches 4 from the left and right. which ended up being 16-c^2 and 4c+20. I then made these expressions equal to each other to solve for the constant c and ended up getting c=-4 and c=8. Neither of these values work, and I'm not quite sure what I should have done.

Use the I.V.T to show that there is a root of the given equation inthe specified interval

tanx=2x (0,1.4)

tanx-2x=0

when f(0) you get 0

When f(1.4) you get 2.99

therefore f(0) <0<f(1.4)

What I did here just seems wrong, there must be more to it than that, but that's all I can get from reading the textbook.

Thanks again

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# Continuity and Intermediate Value Theorem

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