In each exercise 1-9, show that the given functions are linearly independent on (-[infinity], [infinity]).
1. e³ˣ, e⁻²ˣ
2. cos 5x, sin 5x
3. e²ˣ cos x, e²ˣ sin x
4. e⁻ˣ, xe⁻ˣ
5. x²-1, x²+1, x+1
6. eˣ, e²ˣ, e³ˣ
7. e⁴ˣ, xe⁴ˣ, x²e⁴ˣ
8. eˣ, eˣ cos x, eˣ sin x
9. x³, |x|³
10. show that 1/x, x are linearly independent on (0, [infinity]).
11. Show that x+1, x-1, x are linearly dependent on (-[infinity], [infinity])
12. show that sin²x, cos²x, cos 2x are linearly dependent on (-[infinity], [infinity]).
13. show that the two functions in example 2 are linearly dependent on (0, [infinity]).