I don't know how to do both a
and b
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I don't know how to do both a and b 16. The folium of Descartes is the curve C c R2 described by the equation a) Give a parametrization of C. Hint: Use t y/r as parameter b) Compute the area of th...
The figure below shows a curve C, parametrized by (a) The point P lies on C, and its r-coordinate is 4. Find the value of t at the point P according to the parametrization, and find the y-coordinate...
The figure below shows a curve C, parametrized by (a) The point P lies on C, and its r-coordinate is 4. Find the value of t at the point P according to the parametrization, and find the y-coordinate of P. equation in terms of r and y. line 4. as shown shaded in the figure. Find the area of R. (b) The line is normal to C at the point P. Express the line l using an (c) The bounded...
(a) Sketch the curve r(t) = (e cost, e sint) in R2 and compute its are...
(a) Sketch the curve r(t) = (e cost, e sint) in R2 and compute its are length for 0 < t < 87. For the sketch, use of software is acceptable, but the graph should be drawn by hand and the right features should be present.] (b) The vector v makes an angle of with the positive -axis. Write the vector v in component form. Furthermore, write the equation of the line lt') passing through the origin with direction vector...
4. An economy can be described by the following equations: C = 5+.8(Y-T) I = 2-r...
4. An economy can be described by the following equations: C = 5+.8(Y-T) I = 2-r G = 2 T = 2 L(r,Y) = 4 + 4y -.5r M = 2 P=1 Solve algebraically for an equation for the IS curve (with 'r' on the left-hand side). Do the same for the LM curve. Finally, solve for the equilibrium values of 'r' and 'Y' in the ISLM model:
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vect...
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vector r e R2 such that Df(ri, r2) 0. What can we say about the tangent plane to the surface of the graph at (ri,2,f(r1, r2))? (c) How do you know that the Hessian, Df(x, y) is necessarily symmetric? Recall that t,y D2 f(x,y) , y) (d) What are the eigenva of D2f(r1,r2) for each root of the gradient that...
3. [3 marks] Show that for a plane curve described by r = c(t)i + y(t)j,...
3. [3 marks] Show that for a plane curve described by r = c(t)i + y(t)j, the curvature k(t) is I'Y' - YX| (x2 + y2)3/27 where a prime denotes differentiation with respect to t. 4. [2 marks] Let f(x, y) = xy +3. Find (a) f(x + y, x - y); (b) f(xy, 3.22y).
I know the answer of a and b but I don't know hoe to do c dy a) Find- if y = ax +b cx+d b) By using changes of vari...
I know the answer of a and b but I don't know hoe to do c
dy a) Find- if y = ax +b cx+d b) By using changes of variable of the form (*) show that: dx=-in 3--In 2 4 c) Using the ideas from part a) and b) to evaluate the integrals: r2+3x +12 In dx and In o (x + 3)2 (x + 3)2
dy a) Find- if y = ax +b cx+d b) By using changes...
8. (a) Use a graphing utility to graph the curve represented by the following polar equation: r(e)-2cos(3) over the interval 0s0<t. b) Find the area of one petal of this curve. (c) Shade the i...
8. (a) Use a graphing utility to graph the curve represented by the following polar equation: r(e)-2cos(3) over the interval 0s0<t. b) Find the area of one petal of this curve. (c) Shade the interior of the petal whose area you are computing. (Be careful with your notation show orientation arrous on your curve, and show your steps clearly.) (b) area of one petal of this curve-
8. (a) Use a graphing utility to graph the curve represented by the...
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I α(s) sin(θ(t)) dt Use your result to give another geometric interpretation to the (...
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I α(s) sin(θ(t)) dt Use your result to give another geometric interpretation to the (signed) curva- ture and its sign? to) rindy,R-- parmetrised with unit speed suchhat y -0and kt) - s for all seR.
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I...
Can I know how to do part(c)? I know how to do (a)(b). By (a) and...
Can I know how to do part(c)? I know how to do
(a)(b).
By (a) and (b), I get this 4 results.
1. ▾.F = 2xz5-2xz+3xz2
2. ▾xF = (2xy) i + (5x2z4-z3) j
-(2yz) k
3. ▾.(▾xF) = 0
4. ▾x(▾f) = 0
Next, i need to calculate part (c).
I want the solution of part(c), so don't give me the result of
part(a) and (b) again,
thanks!
1. (25 marks) (a) Evaluate . F and V. (V x...
Assume the Chilean economy can be described as follows: C=200+0.25Yd l=150+0.25Y-1000r G=250 T=200 (M/P)d= L(r, Y)...
Assume the Chilean economy can be described as follows: C=200+0.25Yd l=150+0.25Y-1000r G=250 T=200 (M/P)d= L(r, Y) = 2Y- 8000r Ms=1840 P=1 a) Derive the equation for the LM curve. ( 1 .5 mk) b) Determine the slope af the LM curve. (0.5 mark) c) Derive the equation for the IS curve (I.S mk) d) Determine the slope ofthe IS curve. (0.5 mk) c) Compute the quilibrium values of income (Y) and interest rate (R)? (2 marks) [) Calculate the value...
The figure below shows a curve C, parametrized by (a) The point P lies on C, and its r-coordinate is 4. Find the value of t at the point P according to the parametrization, and find the y-coordinate of P. equation in terms of r and y. line 4. as shown shaded in the figure. Find the area of R. (b) The line is normal to C at the point P. Express the line l using an (c) The bounded...
(a) Sketch the curve r(t) = (e cost, e sint) in R2 and compute its are length for 0 < t < 87. For the sketch, use of software is acceptable, but the graph should be drawn by hand and the right features should be present.] (b) The vector v makes an angle of with the positive -axis. Write the vector v in component form. Furthermore, write the equation of the line lt') passing through the origin with direction vector...
4. An economy can be described by the following equations: C = 5+.8(Y-T) I = 2-r G = 2 T = 2 L(r,Y) = 4 + 4y -.5r M = 2 P=1 Solve algebraically for an equation for the IS curve (with 'r' on the left-hand side). Do the same for the LM curve. Finally, solve for the equilibrium values of 'r' and 'Y' in the ISLM model:
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vector r e R2 such that Df(ri, r2) 0. What can we say about the tangent plane to the surface of the graph at (ri,2,f(r1, r2))? (c) How do you know that the Hessian, Df(x, y) is necessarily symmetric? Recall that t,y D2 f(x,y) , y) (d) What are the eigenva of D2f(r1,r2) for each root of the gradient that...
3. [3 marks] Show that for a plane curve described by r = c(t)i + y(t)j, the curvature k(t) is I'Y' - YX| (x2 + y2)3/27 where a prime denotes differentiation with respect to t. 4. [2 marks] Let f(x, y) = xy +3. Find (a) f(x + y, x - y); (b) f(xy, 3.22y).
I know the answer of a and b but I don't know hoe to do c
dy a) Find- if y = ax +b cx+d b) By using changes of variable of the form (*) show that: dx=-in 3--In 2 4 c) Using the ideas from part a) and b) to evaluate the integrals: r2+3x +12 In dx and In o (x + 3)2 (x + 3)2
dy a) Find- if y = ax +b cx+d b) By using changes...
8. (a) Use a graphing utility to graph the curve represented by the following polar equation: r(e)-2cos(3) over the interval 0s0<t. b) Find the area of one petal of this curve. (c) Shade the interior of the petal whose area you are computing. (Be careful with your notation show orientation arrous on your curve, and show your steps clearly.) (b) area of one petal of this curve-
8. (a) Use a graphing utility to graph the curve represented by the...
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I α(s) sin(θ(t)) dt Use your result to give another geometric interpretation to the (signed) curva- ture and its sign? to) rindy,R-- parmetrised with unit speed suchhat y -0and kt) - s for all seR.
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I...
Can I know how to do part(c)? I know how to do
(a)(b).
By (a) and (b), I get this 4 results.
1. ▾.F = 2xz5-2xz+3xz2
2. ▾xF = (2xy) i + (5x2z4-z3) j
-(2yz) k
3. ▾.(▾xF) = 0
4. ▾x(▾f) = 0
Next, i need to calculate part (c).
I want the solution of part(c), so don't give me the result of
part(a) and (b) again,
thanks!
1. (25 marks) (a) Evaluate . F and V. (V x...
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