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Homework Statement
[tex]\mathop {\lim }\limits_{x \to 0 } \frac{1 - cosh(2x)}{{4x^3 + x^2}}[/tex]
Homework Equations
Product, sum, quotient laws
The Attempt at a Solution
[tex]\mathop {\lim }\limits_{x \to 0 } \frac{1 - cosh(2x)}{{4x^3 + x^2}} =
\mathop {\lim }\limits_{x \to 0 } \frac{\lim 1 - \lim cosh(2x)}{{\lim 4 + \lim x^3 + \lim x^2}}
=
\mathop {\lim }\limits_{x \to 0 } \frac{1 - \lim cosh(2x)}{{4 + 0 + 0}}
=
\mathop {\lim }\limits_{x \to 0 } \frac{1 - cosh(\lim 2x)}{{4}}
=
\frac{1 - cosh(0)}{{4}}
= \frac{1 - 1}{{4}}
= 0
[/tex]
However the answer is supposed to be 2.
I was sure the denominator should be 4, but not sure how to get 8 in the numerator