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1. Determine the corresponding rectangular equation: a. x=t?, y=t-1 b. x=...
Find an equation of the line tangent to the curve at the point corresponding to the...
Find an equation of the line tangent to the curve at the point corresponding to the given value of t. 71 x= cost+t sint, y=sint-tcost;t=4 (Type an equation. Simplify your answer. Type your answer in slope-intercept form. Type an exact answer. Use integers or fractions for any numbers in the equation.)
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and...
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
Ae ete (a) Determine the rectangular equation that is parameterized by these equations et -et 2 3...
ae ete (a) Determine the rectangular equation that is parameterized by these equations et -et 2 3. Iet r(t)--and y(t) (Hint: Look at 2 and y?.) (b) Graph the above curve. Be sure to specify the direction of the curve. (c) For what values of t does this curve have a horizontal tangent line? What points in the xy-plane do these values correspond to? (d) For what values of t does this curve have a vertical tangent line? What points...
An object is moving in the plane and has parametric equations (6) 2+1 +1 The corresponding...
An object is moving in the plane and has parametric equations (6) 2+1 +1 The corresponding derivative functions are x) 2/(1+0) YO (2+1) where to is in units of seconds and the units on the coordinate axes are feet (a) The horizontal velocity of the object at time is (b) The vertical Velocity of the object at time is (c) The tangent line to the path is horizontal at time to (d) The object crosses the y-axis at time to...
Find the points (x,y) on the curve C given by x = 1+t? and y =...
Find the points (x,y) on the curve C given by x = 1+t? and y = t- t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes.
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 +...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
x = COST TT 7) Find the slope of the line tangent to at t =...
x = COST TT 7) Find the slope of the line tangent to at t = y = 8 sint 2 1 -" 3 8) Find the length of 0<t<1 1 - 21
you can skip question 1 Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t))...
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is give...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is given by r" for 1 sts 6 a) Use the ratio test to find the interval of convergence of the Maclaurin series for f a) Find the slope of the line tangent to the curve C at the point where t 3. b) Let...
X Incorrect. Use the transformation u = x-10y, v = 10x + y to find x-10y...
X Incorrect. Use the transformation u = x-10y, v = 10x + y to find x-10y dA 10x + y R where R is the rectangular region enclosed by the lines X - 10y = 1, x - 10y = 100, 10x + y = 5, 10x + y = 25. (x-104 dA= TS 9999 -In(5) Edit 2 10x + y R
Find an equation of the line tangent to the curve at the point corresponding to the given value of t. 71 x= cost+t sint, y=sint-tcost;t=4 (Type an equation. Simplify your answer. Type your answer in slope-intercept form. Type an exact answer. Use integers or fractions for any numbers in the equation.)
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
ae ete (a) Determine the rectangular equation that is parameterized by these equations et -et 2 3. Iet r(t)--and y(t) (Hint: Look at 2 and y?.) (b) Graph the above curve. Be sure to specify the direction of the curve. (c) For what values of t does this curve have a horizontal tangent line? What points in the xy-plane do these values correspond to? (d) For what values of t does this curve have a vertical tangent line? What points...
An object is moving in the plane and has parametric equations (6) 2+1 +1 The corresponding derivative functions are x) 2/(1+0) YO (2+1) where to is in units of seconds and the units on the coordinate axes are feet (a) The horizontal velocity of the object at time is (b) The vertical Velocity of the object at time is (c) The tangent line to the path is horizontal at time to (d) The object crosses the y-axis at time to...
Find the points (x,y) on the curve C given by x = 1+t? and y = t- t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes.
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
x = COST TT 7) Find the slope of the line tangent to at t = y = 8 sint 2 1 -" 3 8) Find the length of 0<t<1 1 - 21
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is given by r" for 1 sts 6 a) Use the ratio test to find the interval of convergence of the Maclaurin series for f a) Find the slope of the line tangent to the curve C at the point where t 3. b) Let...
X Incorrect. Use the transformation u = x-10y, v = 10x + y to find x-10y dA 10x + y R where R is the rectangular region enclosed by the lines X - 10y = 1, x - 10y = 100, 10x + y = 5, 10x + y = 25. (x-104 dA= TS 9999 -In(5) Edit 2 10x + y R
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