- #1
scorpa
- 367
- 1
Hello everyone,
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
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