Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\displaystyle\lim_{x\to 0}\,\frac{x+3\sin 5x}{\sin 7x+9x}=$	A. \(1\)
B. \(\frac57\)
C. \(3\)
D. \(\frac19\)
E. \(\frac{15}7\)

$\inline\\\text{Rekening houdend met}\;\displaystyle\lim_{x\to 0}\frac{\sin ax}{bx}=\frac ab\\\displaystyle\lim_{x\to 0}\,\frac{x+3\sin 5x}{\sin 7x+9x}=\lim_{x\to 0}\,\frac{1+3\frac{\sin 5x}{x}}{\frac{\sin 7x}{x}+9}=\lim_{x\to 0}\,\frac{1+3.5}{7+9}=\frac{16}{16}=1$