Ans: 7 ( limit does exist)
Explanation:
The limit exists only if we apply the limits -be it left hand or right hand- the answers to both should be 7 because at x = 0 the value is constant.
Left hand limit( x < 0):
[tex] \lim_{x \to 0} 7-x^2 = 7-(0)^2 = 7[/tex]
Right hand limit (x > 0):
[tex]\lim_{x \to 0} -10x + 7 = -10(0) + 7 = 7[/tex]
Since upon applying the limits, the answers to all is 7 (same). Hence limit exists!
