# math 4 12

4 3 3 predicate_on_list geq list 4 3 3 4≥3≥3 3 3 4 3≤3≤4 a a a ≡ ¬¬a 227 π ≃ 22/7 a b a|b ∫sin=cos a b ∫a b cos x 0 1 x 2 ∫0 1 x 2 d x x expression-in-x int lambda x expression-in-x x x x int lambda x x x C f defint C f x D expression-in-x defint D lambda x expression-in-x x a b expression-in-x defint oriented_interval a b lambda x expression-in-x x y 0 x x 1 0 y y 1 x 2 y 3 defint suchthat cartesianproduct R R and leq 0 x leq x 1 leq 0 y leq y 1 lambda x y times power x 2 power y 3 f f′ x x x d sin⁡x d x = cos⁡x x 2 x 4 d 2 x 4 d x 2 x expression-in-x diff lambda x E x x x diff lambda x sin x x x n expression-in-x nthdiff n lambda x expression-in-x x 2 x x nthdiff 2 lambda x sin x x 1 1 3 f D 1,1,3 f 1 1 3 x y z f x y z ∂3 f⁡x y z ∂x 2 ∂z x y f x y ∂2 f ⁡ x y ∂x ∂y x m y n k f x y ∂k f⁡x y ∂x m ∂y n x1 n1 xk nk total-n1-nk expression-in-x1-xk partialdiffdegree list n1 nk total-n1-nk lambda x1 xk expression-in-x1-xk x1 xk plus n1 nk