Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 6 10v2 + 6 , a = 1 lim v→1 p(v) = lim v→1 6 10v2 + 6 g

1. are the triangles similar and if so why? what is the value of x? show your work.

Explain why the function is discontinuous at the given number a. (select all that apply.) f(x) = 1 x + 1 a = −1 f(−1) is undefined. lim x→−1+ f(x) and lim x→−1− f(x) exist, but are not equal. lim x→−1 f(x) does not exist. f(−1) and lim x→−1 f(x) exist, but are not equal. none of the above

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?