Question

Consider the following statements:
Statement 1: $\underset{x\to 1}{\lim }\frac{a{x}^2+bx+c}{c{x}^2+bx+a}$ is $1($ where $a+b+c\ne 0)$
Statement 2: $\underset{x\to -2}{\lim }\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$ is $\frac{1}{4}$

• A. Only statement 2 is true
• B. Only statement 1 is true
• C. Both statements 1 and 2 are true
• D. Both statements 1 and 2 are false

Answer 1

Answer: (B)

statement 1 is true Statement 2 is false
$\left[\frac{a+b+c}{a+b+c}=1\right]$
$\underset{x\to -2}{\lim }\frac{\frac{1}{x}+\frac{1}{2}}{x+2}\text{ is }-\frac{1}{4}$