Hello everyone,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Continuity and Intermediate Value Theorem

**Physics Forums | Science Articles, Homework Help, Discussion**