Question

Find the limit as x approaches 0 of (3x-sin(kx))/x k can not = 0

Answer 1

\(\bf lim_{x\to 0}\quad \cfrac{3x-sin(kx)}{x}\qquad \textit{multiply by "k"}
\\ \quad \\
\cfrac{3x-sin(kx)}{x}\cdot \cfrac{k}{k}\implies \cfrac{3kx-sin(kx)k}{kx}\implies \cfrac{3kx}{kx}-\cfrac{sin(kx)k}{kx}
\\ \quad \\
\cfrac{3kx}{kx}-\cfrac{sin(kx)}{kx}\cdot k\)

what do you think?

Answer 2

\[\LARGE lim_{x \rightarrow 0}{\dfrac {3x-\sin(kx)}{x}}\]

Answer 3

is that the problem?

Answer 4

\(\LARGE lim_{x \rightarrow 0} {3x\over x} -lim_{x \rightarrow 0} {sin(kx)\over x}\)

Answer 5

\(\LARGE 3 -lim_{x \rightarrow 0} {kcos(kx)\over 1}=k\)