# calculus 3

Anonymous
account_balance_wallet \$120

Question description

please help me with the following calculus 3 problems I need them urgently today. all the questions are in the following pdf

MTH 277 Test 2 – show your work Name 1. Limit and Continuity a. lim(x,y)→(1,2) x2 +y x2 −y 3 ? b. Does lim(x,y,z)→(0,0,0) xy+yz+xz x2 +y 2 +z 2 exist? If yes, what is the limit value? If not, why? 2. Level curve, gradient and directional derivative : a. Let z = f (x, y ) = x2 − xy + y 2 + y , consider the level curve f (x, y ) = 2, what is the gradient ∇f at (1, 1)? b. What is the equation of the tangent line at (1, 1) for f (x, y ) = 2? c. What is the equation of the normal line at (1, 1) for f (x, y ) = 2? d. Given a vector uˆ = ( √12 , - √12 ), what is the directional derivative Dû at (1, 1)? e. Let w = g (x, y , z) = x2 − xyz + y 2 + y + z 2 − 4 , consider the level curve g (x, y , z) = 0, what is the gradient ∇g at (1,− 1, − 2)? f. What is the equation of the tangent plane at (1,− 1, − 2) for g (x, y , z ) = 0? g. Consider the (x, y) points of g (x, y , z) = 0 particles moving along a unit circle C, find a parametric form, i.e. x = u(t), y = v(t) h. Find the velocity on the z direction, i.e. derivative dd zt use the chain rule as a function of t i. Find the acceleration on z direction as a function of t 3. M ixed partial and higher derivatives, chain rule a. Given f (x, y, z) = x3 − x 3y + ln ( yz ) − sin⁡(x) , find the gradient ∇f b. z = f (x, y ) = x3 + y 3 − 6 x2 + 9y 2 + 12x + 27y + 19 ,, find its relative min and max if j. any, and the saddle points Given g(x, y, z) = x2 + y 2 + z 2 = 9, consider (x, z) as particles moving along an elliptical curve 4x 2 + 9z 2 = 1 , find a parametric form as , i.e. x = u(t), z = v(t) k. Find the velocity on the y direction, i.e. derivative dd yt use the chain rule as a function of t l. Find the acceleration on y direction as a function of t 4. Tangent plane and Tangent line a. Given a surface A as x2 − 2x + y 2 + (z − 1)2 = 4, f ind its tangent plane at ( 1,1,3) b. Given a surface B as x2 + y 2 + z = 4, f ind its tangent plane at ( 1,1,3) c. A intersects B on a curve at (1, 1, 3) find the tangent line along this curve (for both A and B) at this point 5. Double integral (over a region), polar coordinate, surface area a. Let f (x, y ) = x2 − xy + y 2 + y , and a region D = [-1, 1] by [-1, 1] for (x , y) find ∬D f (x, y ) da = ? b. Find the volume under the surface z = f (x, y ) = √1 − x2 and above the triangular region formed by y = x, x = 1, and the x-axis c. Find the volume defined by z = f (x, y ) = √4 − x2 − y 2 above the circular region bounded by the two axes and the circle x2 + y 2 = 4 in the first quadrant d. Find the surface area defined by the part c. 6. Triple integral: t​he tetrahedron is defined by corners at (0, 0, 0), (0, 3, 0), (2, 3, 0), and (2, 3, 5) bdf a. If the volume is given by ∫ ∫ ∫ dz dy dx , what are a, b, c, d, e and f? ace bdf b. If the volume is given by ∫ ∫ ∫ dx dy dz , what are a, b, c, d, e and f? ace bdf c. If the volume is given by ∫ ∫ ∫ dy dx dz , what are a, b, c, d, e and f? ace d. Compute the volume use the integral a. e. Compute the volume use the integral b. f. Compute the volume use the integral c. 7. Surface area and Integral Given a right circular cone S with both height and base radius are a a. Write the surface equation f(x, y, z) = 0 b. Find its volume V c. Find its surface area d. Let g(x,y,z) = x+y+z is defined on S, find ∫ ∫ g ds S

tessyjohnston
School: University of Maryland

Are...

flag Report DMCA
Review

Anonymous
Top quality work from this guy! I'll be back!

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors