Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cost) k OT= (-7 sin t)j + (7 cos t)k O T = (-sin t)j + (cos t)k O T=(7 cos t)j - (7 sin t)k O T = - = (sin t)j + = (cos t)k

Q: 4. Find the equation of the tangent line to the graph of f(x)= 2x² – In Vx at x = 1.

A:

Q: TION WORKSHEET 6 n 3: Find the points on the curve X+ Sinx y= at which the tangent is hotizontal.

A: We have to find the points on the curve at which the tangent is horizontal. To find the points on…

Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin (t)) at t = 3…

A:

Q: What is the gradient of the tangent line to the curve y = 2x³ – 3x2 at the point with a = 2? |…

A:

Q: Find the curve y if dy = x2 +5, dx + 5, curve passes through (0, 25)***

A:

Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

A:

Q: Find the directional derivative of J(, 9) + 3y at the point (2, the direction 57 radians.

A:

Q: Consider the folloinwg curve: y = square root of -1+2x At what point on the given curve is the…

A: Consider the folloinwg curve: y = square root of( -1+2x) to find the point on the given curve is the…

Q: Find the vector equation of the tangent line to F(t) = 2 (el-t) In t i+ tan-tj+ k at cos(t m) the…

A: Answer is mentioned below

Q: 7. Two part question: a. Determine the equation for the slope of the secant line between the point…

A: The given problem is solved below in detail.

Q: Find the derivative, r'(t), of the vector function. r(t) at cos(2t)i + b sin5(t)j + c cos³ (t)k…

A: