1a. Find the equation of a tangent line to the curve f(x) =
ln(2−x)/x + 3x at the point (1, 3).
1b. Suppose the following function is defined implicitly by the
equation, Find dy/dx x^2 − 3y^2 + 6e^x = 4x^2y + 5
2. Using only the definition of derivative as a limit, calculate
f(x) where f(x) = 1/x − 5
3. One thousand dollars is invested at a rate of 3%
a) How much money will be in the...
1. Find the equation of the line tangent to the curve y=2x^2 +
sin4x at x= π/3.
2. Determine the point(s) where the tangent line to y= 2sinx-4x
has a slope of-3 in the domain 0≤x≤ 2π.
b) Find the equation of the tangent line.
A) Find the equation of the tangent line to the curve y
= 5e-8x at the point (0, 5).
B) Solve for t.
e0.09t = 9
C) Rancher Johann wants to build a three-sided rectangular fence
near a river, using 280 yards of fencing. Assume that the river
runs straight and that Johann need not fence in the side next to
the river.
Johann wants to build a fence so that the enclosed area is
maximized.
What should be the...
Find the equation of the plane tangent to the function f(x, y) =
(x^2)(y^2) cos(xy) at x = y = π / √ 2 . Using this linearization to
approximate f, how good is the approximation L(x, y) ≈ f(x, y) at x
= y = π / √ 2 ? At x = y = 0? At (x, y) = (π, π)?