Question

Match the given limits to their numerical value.

• A. 3
• B. 12
• C. 4
• D. 0.0

Answer 1

$i)\underset{x\to 0}{lim}\frac{e^{3x}-1}{x}=\underset{x\to 0}{lim}\frac{3e^{3x}}{1}=3e^0=1$

$ii)\underset{x\to 0}{lim}\frac{1-cosx}{x^2}=\underset{x\to 0}{lim}\frac{sinx}{2x}=\underset{x\to 0}{lim}\frac{cosx}{2}=\frac{1}{2}$

$iii)\underset{x\to 0}{lim}\frac{sin4x}{x}=\underset{x\to 0}{lim}\frac{4cos4x}{1}=4$

$iv)\underset{x\to \infty }{lim}\frac{x^2}{e^x}=\underset{x\to \infty }{lim}\frac{2x}{e^x}=\underset{x\to \infty }{lim}\frac{2}{e^x}=0$