true or false, limx→0 sin(−9x)/e^6x−7 = −3/2\nfalse\ntrue
true or false, limx→0 sin(−9x)/e^6x−7 = −3/2\nfalse\ntrue
Answer
Explanation:
Step1: Evaluate numerator and denominator at $x = 0$
When $x\rightarrow0$, $\sin(-9x)\rightarrow\sin(0) = 0$ and $e^{6x}-7\rightarrow e^{0}-7=1 - 7=-6$.
Step2: Use L - H rule (if applicable)
Since $\frac{\sin(-9x)}{e^{6x}-7}$ is in the $\frac{0}{- 6}$ form (not an indeterminate $\frac{0}{0}$ or $\frac{\infty}{\infty}$ form), we don't need L - H rule. $\lim_{x\rightarrow0}\frac{\sin(-9x)}{e^{6x}-7}=\frac{\sin(0)}{e^{0}-7}=\frac{0}{1 - 7}=0\neq-\frac{3}{2}$
Answer:
False