Question

Lim x-1 x2 - 1/ sin(x-2)

Answer 1

`\lim_(x \to 1)(x^2-1)/(sin(x-2))=0`

Step-by-step explanation:

Assuming the correct expression is to find the following limit:

`\lim_(x \to 1)(x^2-1)/(sin(x-2))`

Use the property the limit of the quotient is the quotient of the limits:

`\lim_(x \to 1)(x^2-1)/(sin(x-2))=(\lim_(x \to 1)x^2-1)/(\lim_(x \to 1)sin(x-2))`

Evaluate the numerator:

`(\lim_(x \to 1)x^2-1)/(\lim_(x \to 1)sin(x-2))=(1^2-1)/(\lim_(x \to1)sin(x-2))=(0)/(\lim_(x \to 1)sin(x-2)`

Evaluate the denominator:

• Since
  `\lim_(x \to1)sin(x-2)\\eq 0`

`(0)/(\lim_(x \to1)sin(x-2))=0`