1.Find the slope of the curve r = cos(2theta ) at theta =pi/6 ..................

Question

1.Find the slope of the curve r=cos(2theta) at theta =pi/6

...................

2. If x=2t-1 and y=3-4t^2, then dy/dx is

....................

3.Write the equation for the line tangent to the curve defined by F(t) = (t2 +1, 2t ) at the point where y=4.

A. y-4=ln2(x-2)

B. y-4=4ln2(x-2)

C. y-4= 4(x-5)

D. y-4=ln2(x-5)

E. y-4=4ln2(x-5)

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4. Sketch the curves (t^2, -2t+1) and (sin(t), cos(t)). The curves

A. do not intersect

B. intersect exactly once

C. intersect exactly twice

D. intersect three times

...................................

5. Sketch the curves (t + 3, -2t+ 1) and (sin(t), cos(t)). The curves

A. do not intersect

B. intersect exactly once

C. intersect exactly twice

D. intersect three times

.................................

6. Give the point of intersection of the curves (t + 3, -2t + 1) and (-3t + 1, 3t -4)

A. (7/2,0)

B. (10,10)

C. (10,-13)

D. (4,-1)

Explanation / Answer

1.) r' = -2 sin (2 theta)

at theta = pi/6

we get

slope = r' = -2 sin(2pi/6)

             = -2 sin(pi/3)

                = -sqrt 3

slope = -1.732

2.) dy/dt = -8t

dx/dt = 2

dy/dx = dy/dt * dt/dx = -4t

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