We consider the following functions:
H (x) = (x ² +2 x) sin (2 / x) g (x) = x / a * [b / x] and f (x) = x ² ([1 / x] + [1 / x ²])
a, b belong IR * +
a: Show that for every x * + = IR)-2x ² + x is less than f (x) -1 and f (x) -1 is a lower x ..
b Concluded limit f en0
c: Show that for any x in IR + *:-x / a is less than g (x)-b / a and
g (x)-b / a
is less than or equal to 0
d: Concluded limit g 0
e: Show that for any x in] -1,1 [: | h (x) | ≤ 3 | x |
f: Concluded limit h 0

Question

We consider the following functions: 
H (x) = (x ² +2 x) sin (2 / x) g (x) = x / a * [b / x] and f (x) = x ² ([1 / x] + [1 / x ²]) 
a, b belong IR * + 
a: Show that for every x * + = IR)-2x ² + x is less than f (x) -1 and f (x) -1 is a lower x .. 
b Concluded limit f en0 
c: Show that for any x in IR + *:-x / a is less than g (x)-b / a and 
g (x)-b / a 
is less than or equal to 0 
d: Concluded limit g 0 
e: Show that for any x in] -1,1 [: | h (x) | ≤ 3 | x | 
f: Concluded limit h 0

anonymous · Answer

a: prove $$-2x²+x <f(x)-1<x$$