Use IVT to prove solutions exist for cos x = x on (0,1), ln x = e^(-x) on (1,2)

[gurbanoğlu]

Use the IVT to show that there is a solution to the given functions on the given intervals.
a. cos x = x, (0,1)

b. ln x = e^(-x) (1,2)

Please help explain and solve these I really need it for my class.

 

[ksdhart2]

What are your thoughts? What have you tried? If you're stuck at the very beginning and don't even know where to start, I'd suggest reviewing the definition of the intermediate value theorem. If you're finding your class notes and/or textbook to be insufficient, you might try Googling "intermediate value theorem." Many, many resources on this topic are available. I found one such page herehttps://www.mathsisfun.com/algebra/intermediate-value-theorem.html. Please share with us any and all efforts you've made on these problems, even the parts you know for sure are wrong. Thank you.