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I gave my students a question that said
if
[tex]\lim _{x \rightarrow 2 } \frac{f(x)}{x^2-4} = 7 [/tex]
find the limit
[tex]\lim_{x\rightarrow 2 } \frac{f(x)}{x-2 } [/tex]
one of my students answered like this
from the given
[tex]\frac{f(x)}{x^2-4} = 7 \Rightarrow f(x) = 7(x^2-4) [/tex]
then he complete the solution
[tex]\lim_{x\rightarrow 2} \frac{7(x-2)(x+2)}{x-2} = 28 [/tex]
which is true, what he did in this
[tex]\frac{f(x)}{x^2-4} = 7 \Rightarrow f(x) = 7(x^2-4) [/tex]
is not true 100%, it is true around 2
What is your opinion ?
Thanks in advance
if
[tex]\lim _{x \rightarrow 2 } \frac{f(x)}{x^2-4} = 7 [/tex]
find the limit
[tex]\lim_{x\rightarrow 2 } \frac{f(x)}{x-2 } [/tex]
one of my students answered like this
from the given
[tex]\frac{f(x)}{x^2-4} = 7 \Rightarrow f(x) = 7(x^2-4) [/tex]
then he complete the solution
[tex]\lim_{x\rightarrow 2} \frac{7(x-2)(x+2)}{x-2} = 28 [/tex]
which is true, what he did in this
[tex]\frac{f(x)}{x^2-4} = 7 \Rightarrow f(x) = 7(x^2-4) [/tex]
is not true 100%, it is true around 2
What is your opinion ?
Thanks in advance