7. Find $$ \lim _{x \rightarrow 2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} $$ 8. If $$ f(x)=x^{2}+10 \sin x $$, show that there is a number $$ c $$ such that $$ f(x)=1000 $$

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Floyd Ingram · Accepted Answer

The limit is 0.5. For the function $$ f(x)=x^{2}+10 \sin x $$, there is a number $$ c $$ such that $$ f(c)=1000 $$, but it cannot be found directly and requires numerical methods.

7. Find \( \lim _{x \rightarrow 2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} \) 8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \)

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7. Find \( \lim _{x \rightarrow 2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} \) 8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \)

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