For the curve given by r(t) = (8sin(t), -3t, -8cos(t)), find the unit tangent.

Q: Find an equation of the line tangent to each of the following curve at the given point. y + Vxy = 6;…

A:

Q: Find ​(a) the slope of the curve at the given point​ P, and ​(b) an equation of the tangent line at…

A:

Q: B) Find all the points on the curve y=tan x, -n/2<x</2, where the tangent line is parallel to the…

A:

Q: Find the equation of the tangent line to the curve y = at 1+7e What is the equation of the line…

A:

Q: Find a.) the slope of the curve at the given point P, and b.) an equation of the tangent line at P.…

A: Find a.) the slope of the curve at the given point P We have given the curve y=x2 – 5 and a point…

Q: :If the tangent at (a, b) to the curve x³ + y° = c° meet the curve again in (a,,b,). b, Prove that…

A:

Q: find (a) the slopeof the curve at the given point P, and (b) an equation of the tangentline at P. y…

A: Given curve:

Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: The given function is y=x2-4x and the point is 1,-3

Q: Find the equation of the line that is tangent to the curve r = r In y, I> 0, at the point (1.e).

A:

Q: The curves y = x2 + ax + b and y = cx - x2 have a common tangent line at the point (1, 0). Find a,…

A:

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2…

A: Solution is here

Q: For the curve r= 2+ 2coS o : © Find dy ) Find the ne slope of the tangent line to the curve at o =II…

A:

Q: Find the equation for (a) the tangent plane and (b

A: Given, the surface                      4z-x2=0 and the point P0(4, 0, 4).

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=π/2 in the given function  Since both sides are equal so (1, π/2) is on the curve…

Q: The equation of the tangent line to the curve at the given point. x2 v2 2-13 = (1, 1) is %3D 100 4…

A:

Q: Find the values of a and b for the curve x2y + ay? = b if the point (1,1) is on its graph and the…

A: The slope of the tangent 'm' at a point (x1,y1) for a curve S(x,y) Is given by dydxx1,y1 therefore…

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A:

Q: 30. Find the points on the curve y = tan x, -7/2 <x< T/2, where the tangent is parallel to the line…

A:

Q: For the curve x2 + 6y² = -2 find the equation of: a) the tangent line at (2, 1) b) the normal line…

A:

Q: find (a) the slopeof the curve at the given point P, and (b) an equation of the tangentline at P. y…

A: Given equation of curve is y=x Given point is P(4,2). (a) Differentiating the given curve with…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

A:

Q: Find the equation of the tangent line to the curve (a lemniscate) 2 2(a? + y?) = 25(æ² – y²) at the…

A: Topic:- application of derivatives

Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: The given function is y=x3 and the point is 2,8.

Q: Show that the equation of the tangent to the curve = 2 (a'0, b1.0) a y at the point (a, b) is = 2.…

A:

Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A:

Q: Given the function z = = f(x,y) = 2y³ -5xy-3x²+2, find the equation of the tangent plane at (1,-1),…

A: Given problem:- Given the function z  = f(x, y) = 2y³ −5xy-3x²+2, find the equation of the tangent…

Q: given x3   + y3 -9xy = 0,   find the point where the curve has a vertical tangent line

A:

Q: If a curve is given by x(t)= t3 - 4t2 + 4t +3 and y(t)=t+3, then the equation of the line tangent to…

A: No. The line is not tangent to the curve at the point (3,5). The following picture shows the graph…

Q: Given the function f(x)=−2xcos(x), find f′(x). Then find the equation of the tangent line at at the…

A:

Q: find an equation for (a) the tangent line to the curve at P and (b) the horizontal tangent line to…

A:

Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: Find the exact length of the curve. x = et + e=t, y = 5 – 2t, 0st< 4

A: The solution are next step

Q: For the cruciform in the figure below, the equation is x²y2 - 9x2 – 4y2 = 0, find the equation of…

A: To find the equation of the tangent line for the given curve.

Q: The slope of the tangent line at any point (x, y) on a curve is If the point (9, 3) is on the curve,…

A:

Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: a) find the slope of curve at point P(1,-3).Find the derivative of the following function.

Q: Find the slope and concavity of the curves at the given points. r = sin θ,θ = π/6, π/3

A:

Q: Find equations for the tangents to the circle (x - 2)2 + ( y - 1)2 = 5 at the points where the…

A:

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A:

Q: Find the points on the curve where the tangent is horizontal or vertical. r = t - 3t, y = t?- 3.

A:

Q: 2. 7(t) = at t = 0

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: 1.) Given 4x?– y? = 36, find its tangent line equation that must be perpendicular to the line…

A: Given:- curve :- 4x2-y2=36 Line:- 5x-2y-4=0 To find:- Given 4x² - y² = 36, find its tangent line…

Q: Determine the slope of the tangent line, then find the equation of the tangent line at t=pi/6.…

A:

Q: (a) The curve with equation y? = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the…

A: To determine the equation of tangent line.

Q: The equation of the tangent line to the curve a? +y = 25, at (8,-12) is. 12 (x+8) – 12 8 y = 8. y =…

A:

Q: , The equation y2(y? – 4) = x²(x² – 5) is known as the devil's curve. Give an equation for the…

A:

Q: find equations for the lines that are tangent andnormal to the level curve ƒ(x, y) = c at the point…

A: given: ƒ(x, y) = c at the point P0 y - sin x = 1, P0(π, 1)

Q: Find the value of 'a' for which the tangent to the curve ƒ(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

A: