Dtermine the equation of the tangent at the point -2 -5 -

Question

Question 1:

For the curve y = 1 + x - x² determine the equation of the tangent at the point (-2, -5).

Question 2:

Write theorem 2: the Integral of a Constant.

Question 3:

A train moves along a track at a steady 65 miles per hour from 7:00A.M. to10:00 A.M. Express its total distance travelled between this interval as an integral. Evaluate theintegral using Theorem 2.

Question 4:

In the relationship z = f(x, y), identify the dependent and independent variables.

Question 5:

Find ∂z/∂x and ∂z/∂y of, z=x² + 3xy + y -1.

Question 6:

Determine the general solution of the following equation:

(d²y)/(dt² )-3 dy/dt - 18y = 0