Find an equation of the tangent to the curve x = 2 + ln t, y =
t2 + 4 at the point (2, 5) by two methods.
(a) without eliminating the parameter
(b) by first eliminating the parameter
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.
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)?
Find the equation of
the tangent line at x=2 to the graph of
y= x^2-x-7
Write your answer as a
simplified slope-intercept equation y=mx+b.
For
example y=7x-8