Find the unit tangent vector to the curve defined by (t) = (3t, -2t, √√4-12) at t = 1. T(1) = Use the unit tangent vector to write the parametric equations of a tangent line to the curve at t = 1. x(t) y(t) = z(t) = =

Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

Use the parametric equations x= sec(t) , y=tan(t), for -pi/2 < t < pi/2. Sketch the curve represented by the parametric equations (include the orientation of the curve) and write the corresponding rectangular equation by eliminating the parameter and Find the equation of the tangent line to the curve at t = pi/4

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Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the slope of the tangent line to the curve when t = 1. Enter your answer as an exact value in decimal form.

1. a) Find dy for the equation 4x²y² - x³y=3 dx b) find the x-coordinate of each point on the curve where the tangent line is vertical () Find the y-coordinate of each point on the curve. with an x-coordinate of -1.

Find an equation, in slope-intercept form, of the line tangent to the curve with parametric equations x = t²+2t and y = 2 lnt at the point (3,0). y =

A) Find an equation of the line tangent to the function of x? + (y - x)² = 9 atx = 1.

Find the equation of the tangent plane to the graph of Glu, w) — - сos (uw) at the point (5. ). (Use symbolic notation and fractions where needed. Enter your answer using u-, w-, z-coordinates.) the equation: