For the curve given by r(t) = (5 sint, -5t, -5 cos t), find the unit tangent vector and the curvature T(t) = ( k(t) = Add Work

Q: For the curve given by r(t) = (9 sin(t), -2t, -9 cos(t)), Find the unit tangent T(t) = (000) Find…

A: For the curve given by , to find the unit tangent vector, unit normal vector, and the curvature.

Q: Consider the following parametric curve r(t) =

A: Let rt be the parametric equation of the curve. To calculate the unit tangent vector, use the…

Q: Explain why a circle tangent to y=sin(x) at x=π/2 has its center on the vertical line x=π/2. Find…

A: The objective of this question is to understand why a circle tangent to the function y = sin(x) at x…

Q: For r=1+2cos(theta) Determine the points where the tangent line is vertical, By finding the angles,…

A: We will use integral to find area and arc length of polar curve  Note: maximum 3 subpart are allowed…

Q: For the equation x² +2.xy – 3y =0, find the equation of the normal to the tangent line at the point…

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Q: Let f(x, y) = 5ex - Y. Find the equation for the tangent plane to the graph of f at the point (5,…

A: Given: fx, y=5ex-y. To Find: Equation of tangent plane to the graph of f at the point 5, 5.

Q: Find the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

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

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Q: Set a = 1. Plot the helix r(t) together with the tangent line to the curve at

A: let the helix be rt=cosati∧+sinat j∧+btk∧.it is given that a=1 and the interval is 0≤t≤4π.tangent…

Q: For the curve given by r(t) = (-2 sin(t), −1t, 2 cos(t)), Find the unit tangent T(t) = (0) 00 Find…

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Q: The curve is described by V(t)=Vm*sin(w*t+theta). Given V1= 7 volts, V2=-V1, theta=17.900 degrees,…

A: To find all parameter of given graph we need to first find Vm then use time period to find angular…

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: 3. For the curve x – xy² = 8e²4, do the following | a) Verify that the point (2,0) is on this curve.

A: Given, curve x3-xy2=8e2y

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: What are the coordinates of the point on the curve f(x)=x- 4 where the tangent is horizontal?

A: To find the co-ordinates of the point ..

Q: For the smooth curve r(t), find the parametric equations for the line tangent to r at the given…

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