Question

1) x = t^3 + 1 , y = t^2 - t , Find an equation of the tangent to the curve at the point corresponding to t = 1

2) x = t^2 + 1 , y = 3t^2 + t ,Find

a) dy/dx ,

b) (d^2)y / dx^2

c) For which values of t is the curve concave upward?

3) sketch the curve: r = 1 - 3cos θ

4)A demand curve is given by p = 450/(x + 8). Find the consumer surplus when the selling price is $15. Round the final answer to nearest cents.

Answer #1

Please post the other questions as separate questions.

Consider the parametric curve defined by x = 3t − t^3 , y = 3t^2
. (a) Find dy/dx in terms of t.
(b) Write the equations of the horizontal tangent lines to the
curve
(c) Write the equations of the vertical tangent lines to the
curve.
(d) Using the results in (a), (b) and (c), sketch the curve for
−2 ≤ t ≤ 2.

Consider the parametric equations x = 5 - t^2 , y = t^3 - 48t a.
Find dy dx and d 2y dx2 , and determine for what values of t is the
curve concave up, and when is it concave down. b. Find where is the
tangent line horizontal, and where is it vertical.

1.Given that y = x + tan−1 y , find dy dx
2.Determine the equation of the tangent line to the curve y = (2
+ x) e −x at the point (0, 2)

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

Consider x^2 +sin(y)=4xy^2 +1
a.)Use Implicit differentiation to find dy/dx
b.) find an equation tangent of the line to the curve x^2
+sin(y)=4xy^2 +1 at (1,0)

a) Find the equation of the tangent line to the curve x= 2sin2t,
y= 3sint at the point where the same.
b) Find the points on the curve x= t^2-t+2, y=t^3-3t where the
tangent is horizontal.

Use implicit differentiation to find dy dx for x^2 y^3 + 3y^2 −
5x = −10.
(b) Find the equation of the line tangent to the curve in part
a) at the point (1, 2).

Find the exact length of the curve. x = 8 + 9t2, y = 3 + 6t3, 0
≤ t ≤ 5
Find an equation of the tangent to the curve at the given point
by both eliminating the parameter and without eliminating the
parameter. x = 6 + ln(t), y = t2 + 1, (6, 2) y =
Find dy/dx. x = t 3 + t , y = 3 + t
Find the distance traveled by a particle...

3. Consider the equation:
x^2y −√y = 2 + 4x^2
a) Find dy/dx using implicit differentiation. b)Construct the
equation of the tangent line to the graph of this equation at the
point (1, 9)

Find dy/dx and d2y/dx2 for the given parametric curve. For which
values of t is the curve concave upward? x = t3 + 1, y = t2 − t

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