This is an indeterminate form and I think I should use the fact that \$x-2/sin(x-2) = 1 ;\$but idk how to vày that.

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\$\$lim_x o 2 fracx^2-4sin(x-2) = lim_x o 2 left( (x+2) fracx-2sin(x-2) ight) = left( lim_x o2 (x+2) ight) left( lim_x o2 fracx-2sin(x-2) ight)\$\$

The second limit may be written as \$displaystylelim_u o0 frac u sin u\$ và you"ve probably seen that limit evaluated by squeezing.

Hint:

While \$alphasim 0\$, for example when \$alpha o 0\$, then \$sin(alpha)sim alpha\$. Here \$x o 2\$ so we have \$\$(x-2) o 0\$\$

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