Correct Answer - Option 3 : 7
CONCEPT:
If \(\mathop {\lim }\limits_{x \to a} f\left( x \right)\) does not result into indeterminate form, then we use direct substitution in order to find the limits.
The are 7 indeterminate forms which are as follows:
- \((\frac{0}{0})\)
- \(\left( {\frac{{ \pm ∞ }}{{ \pm ∞ }}} \right)\)
- (∞ - ∞)
- (0 × ∞)
- 00
- 1∞
- ∞0
CALCULATION:
Given: \(\mathop {\lim }\limits_{x \to 7} g\left( x \right) = k\) where \(g(x) = \sqrt {8x - 7}\)
As we know that, if \(\mathop {\lim }\limits_{x \to a} f\left( x \right)\)does not result into indeterminate form, then we use direct substitution in order to find the limits.
Here, also we can see that \(\mathop {\lim }\limits_{x \to 7} g\left( x \right)\) does not result into any indeterminate form
So, we can substitute x = 7 in the expression \(g(x) = \sqrt {8x - 7}\) in order to find the value of k
⇒ \(\mathop {\lim }\limits_{x \to 7} \sqrt {8x -7} = 7 = k\)
Hence, option C is the correct answer.
