Question

Help on Limits. Explanation required. *Question attached below* Will give medal and fan :)

Answer 1

\[\lim_{x \rightarrow \infty}\frac{ 3-x^4 }{ x^3+2 }\]
divide the numerator and denominator by x^4 and take limits
\[\frac{ 1 }{ x^3 },\frac{ 1 }{ x^4 },\frac{ 1 }{ x } \rightarrow0~as~x \rightarrow \infty\]

Answer 2

\[\lim_{x \rightarrow 5}\left\{ 3f \left( x \right) \right\}=9\]
\[\lim_{x \rightarrow 5}\frac{ f \left( x \right) }{ 3x-2f \left( x \right) }\]
multiply the numerator and denominator by 3 and take limits.

Answer 3

\[\lim_{x \rightarrow 4}\left\{ x^2+2f \left( x \right) \right\}=10,4^2+2\lim_{x \rightarrow 4}f \left(x \right)=10\]
\[\lim_{x \rightarrow 4}f \left( x \right)=\frac{ 10-16 }{ 2 }=-3 \]
now solve the question.

Answer 4

\[\lim_{x \rightarrow 2}\frac{ ax^2-2 }{ x+3 }=2\]
plug x=2 and calculate the value of a

Answer 5

I ended up with a=0? @surjithayer

Answer 6

\[\frac{ 4a-2 }{ 2+3 }=2,4a-2=2*5=10,4a=10+2=12,a=3\]