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Prove by the epsilon-delta definition of continuity that cos(x) is continuous for an c in reals. Prove that the equation e^x=cos(x) has two...

"1. Prove by the epsilon-delta definition of continuity that cos(x) is continuous for an c in reals.

2. Prove that the equation e^x=cos(x) has two solutions in the interval [-pi/2,0]"

3. Find a function f: R->R that is discontinuous at everal real number, but f^2 is continuous on R
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Question number 1
For given > 0 if
| cos x − cos c| = |2 sin
that is
≤ 2max.(sin c−x
x+c
. sin
|
2
2 x + c |c − x|
|c − x|
).
= 2.1.
2
2
2 Hence we have
| cos x − cos c| ≤ |c −...

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