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The curve Cis given parametrically by x = t2, y = y(t), and intere'. Find the...
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...
8) Find the points (x,y) on the curve given by x = 1+t2 and y=t-t3 where...
8) Find the points (x,y) on the curve given by x = 1+t2 and y=t-t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let-2 st s 2 to see the full curve and to estimate where these points are. Points
8) Find the points (x,y) on the curve C given by x = 1+ t2 and...
8) Find the points (x,y) on the curve C given by x = 1+ t2 and y = t – t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let -2 st s 2 to see the full curve and to estimate where these points are. Points
[8 points) For the curve given by x = t4 – t, y = Int +...
[8 points) For the curve given by x = t4 – t, y = Int + t2, find the equation of the tangent line to the curve at the point (0,1).
Question 14 5 pts Consider the parametrically defined curve a. x = 6sin(3t), y=t, z =...
Question 14 5 pts Consider the parametrically defined curve a. x = 6sin(3t), y=t, z = 6cos(3t); (0,71,- 6) Find the equation of the osculating plane of the curve at the given point 4x + 18y = 18 b. X + 18y = 1871 4x - y = - 1871 d. X - 18y = - 1871 x + 18y = - 1871 C. e. a Ob С Od e
5. Let C be the curve in space given parametrically, by the equations. = - 31+5,...
5. Let C be the curve in space given parametrically, by the equations. = - 31+5, y = ( -2) and 3 = ' + - where 0 < < I and F be the vector field F(1, y) = ri+ j+yk. Find .F.dr.
12. Let a curve be defined parametrically by x(1) = 3cost, y(t) = 3 sint, z(1)-...
12. Let a curve be defined parametrically by x(1) = 3cost, y(t) = 3 sint, z(1)- 21. a) Find the equation of the tangent line to the curve att b) Find the curvature of the curve att
17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work) 17) Let Rbe the reg...
17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work)
17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work)
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.
(3) Find the area bounded by the curve x(t) = 3t-t2, y(t) = 3.li and the...
(3) Find the area bounded by the curve x(t) = 3t-t2, y(t) = 3.li and the y-axis. 3 N 1 2
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...
8) Find the points (x,y) on the curve given by x = 1+t2 and y=t-t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let-2 st s 2 to see the full curve and to estimate where these points are. Points
8) Find the points (x,y) on the curve C given by x = 1+ t2 and y = t – t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let -2 st s 2 to see the full curve and to estimate where these points are. Points
[8 points) For the curve given by x = t4 – t, y = Int + t2, find the equation of the tangent line to the curve at the point (0,1).
Question 14 5 pts Consider the parametrically defined curve a. x = 6sin(3t), y=t, z = 6cos(3t); (0,71,- 6) Find the equation of the osculating plane of the curve at the given point 4x + 18y = 18 b. X + 18y = 1871 4x - y = - 1871 d. X - 18y = - 1871 x + 18y = - 1871 C. e. a Ob С Od e
5. Let C be the curve in space given parametrically, by the equations. = - 31+5, y = ( -2) and 3 = ' + - where 0 < < I and F be the vector field F(1, y) = ri+ j+yk. Find .F.dr.
12. Let a curve be defined parametrically by x(1) = 3cost, y(t) = 3 sint, z(1)- 21. a) Find the equation of the tangent line to the curve att b) Find the curvature of the curve att
17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work)
17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work)
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.
(3) Find the area bounded by the curve x(t) = 3t-t2, y(t) = 3.li and the y-axis. 3 N 1 2
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