Question

Let ( f ) be a function defined for all ( x ) and continuous at all values of ( x ) except at ( x=-2 ) and ( x=0 . ) Suppose that for all ( x>10,4 leq f(x) leq frac{4 x^{2}+x}{x^{2}-4} ) and that the following limits are known: - ( lim _{x ightarrow-2^{-}} f(x)=3 ) - ( lim _{x ightarrow-2^{+}} f(x)=f(2)=1 ) - ( lim _{x ightarrow 0^{-}} f(x)=-4 ) - ( lim _{x ightarrow 0^{+}} f(x)=2 ) Complete the following questions: a) Does there always exist a value ( c ) on the interval ( [-3,0] ) such that ( f(c)=0 ) ? Justify your answer. b) Does there always exist a value ( c ) on the interval ( [-1,1] ) such that ( f(c)=0 ? ) Justify your answer. c) Evaluate ( lim _{x ightarrow infty} f(x) )

          Let ( f ) be a function defined for all ( x ) and continuous at all values of ( x ) except at ( x=-2 ) and ( x=0 . ) Suppose that for all ( x>10,4 leq f(x) leq frac{4 x^{2}+x}{x^{2}-4} ) and that the following limits are known:
- ( lim _{x 
ightarrow-2^{-}} f(x)=3 )
- ( lim _{x 
ightarrow-2^{+}} f(x)=f(2)=1 )
- ( lim _{x 
ightarrow 0^{-}} f(x)=-4 )
- ( lim _{x 
ightarrow 0^{+}} f(x)=2 )
Complete the following questions:
a) Does there always exist a value ( c ) on the interval ( [-3,0] ) such that ( f(c)=0 ) ? Justify your answer.
b) Does there always exist a value ( c ) on the interval ( [-1,1] ) such that ( f(c)=0 ? ) Justify your answer.
c) Evaluate ( lim _{x 
ightarrow infty} f(x) )

$Let ( f ) be a function defined for all ( x ) and continuous at all values of ( x ) except at ( x=-2 ) and ( x=0 . ) Suppose that for all ( x>10,4 leq f(x) leq frac4 x^2+xx^2-4 ) and that the following limits are known: - ( lim x ightarrow-2^- f(x)=3 ) - ( lim x ightarrow-2^+ f(x)=f(2)=1 ) - ( lim x ightarrow 0^- f(x)=-4 ) - ( lim x ightarrow 0^+ f(x)=2 ) Complete the following questions: a) Does there always exist a value ( c ) on the interval ( [-3,0] ) such that ( f(c)=0 ) ? Justify your answer. b) Does there always exist a value ( c ) on the interval ( [-1,1] ) such that ( f(c)=0 ? ) Justify your answer. c) Evaluate ( lim x ightarrow infty f(x) )$

Added by Ngan L.

Question

Please give Ace some feedback