For Applied mathematics part - i don't know all uses of this field, but for example applied mathematics sub-field Optimization - is used in problems such as to find shortest path in map. Some games which requires optimal cooperative strategy may depend on Game Theory sub-field.
For Calculus part - If some developer need to implement *really* solid game physics engine - he/she must have calculus knowledge in one way or the other. You can read this book about physics engine development.
Ever think about the math required to position and orient an object in 3D space? If you're not familiar with terms like vector, matrix, and quaternion, look 'em up. Each one of them is used in 3D math.