2.0. According to the definition of limit, this is a discontinuous function at (0, 1).

3.0, x2 sin1/x2 = (sin1/x2)/(1/x2), so that t= 1/x2, sint/t, t tends to infinity and sint is finite.

4.[f(0)-f(-δx)]/δx, is it x-> 0 instead of δx-> 0? If it is Δ x, the answer is f'(x)

Fifth, the first jump is discontinuous, and the left and right limits exist and are not equal. 1 on the left, 2 on the right.

(-2,4), the normal is parallel, that is, the tangent is vertical, and the tangent slope is derivative, that is, the point where the derivative is equal to -4, y'=2x, and x=-2.

Seven, x > 0, the value is π/2, x.

Eight,

I. 0，x-> 0，sinx

Second,

Eight, two is a long time, have time to forget to answer some concepts.

Eight, e y = 1/2e 2x+ 1/2, dy/dx = e 2x-y = e 2x/e y, e ydy = e 2xdx, both sides are integrated at the same time, eyy = 65438.

Second,-1/2e, using Robida's law, lime-cos 2x * (-sinx)/2x = lim-e-1/2e =-1/2e.

I'm exhausted. I have to get extra points