Final answer to the problem
indeterminate
Step-by-step Solution
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1
Evaluate the limit $\lim_{x\to4}\left(\frac{3x^2-8x-16}{2x^2-9x+4}\right)$ by replacing all occurrences of $x$ by $4$
$\frac{3\cdot 4^2-8\cdot 4-16}{2\cdot 4^2-9\cdot 4+4}$
2
Multiply $-9$ times $4$
$\frac{3\cdot 4^2-8\cdot 4-16}{2\cdot 4^2-36+4}$
3
Subtract the values $4$ and $-36$
$\frac{3\cdot 4^2-8\cdot 4-16}{-32+2\cdot 4^2}$
4
Multiply $-8$ times $4$
$\frac{3\cdot 4^2-32-16}{-32+2\cdot 4^2}$
5
Subtract the values $-32$ and $-16$
$\frac{-48+3\cdot 4^2}{-32+2\cdot 4^2}$
6
Calculate the power $4^2$
$\frac{-48+3\cdot 4^2}{-32+2\cdot 16}$
7
Multiply $2$ times $16$
$\frac{-48+3\cdot 4^2}{-32+32}$
8
Subtract the values $32$ and $-32$
$\frac{-48+3\cdot 4^2}{0}$
9
Calculate the power $4^2$
$\frac{-48+3\cdot 16}{0}$
10
Multiply $3$ times $16$
$\frac{-48+48}{0}$
11
Subtract the values $48$ and $-48$
$\frac{0}{0}$
12
$\frac{0}{0}$ represents an indeterminate form
indeterminate
Final answer to the problem
indeterminate