Homework Answers
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4...
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx
5. (2 Points) Let -2 -y F (x2+y2+z2)2/3' (2+y2)2/3' (r2+y2+22)2/3 Find the work done by this...
5. (2 Points) Let -2 -y F (x2+y2+z2)2/3' (2+y2)2/3' (r2+y2+22)2/3 Find the work done by this force field on an F(t) = (1+3t, 1 + 4t2, 1 +5t3) object that moves from (1,1, 1) to (4,5,6) along the curve
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z =...
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z = 2x2 + 2xy + y2 + 1 at the point P(-1, -3, 18). 2) Find all critical value(s) and classify as maxima/minima/saddle points/none. F(x,y) = 2x + 4y - x2 - y2 - 3 3) Find the directional derivative of z = xy +x in the direction of v= <3,-4> at the point Q(1,4). Also find the direction of maximum increase at this point....
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the...
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
3. A 180-Ib person jumps out of an airplane with initial upward velocity of 5 ft/s...
3. A 180-Ib person jumps out of an airplane with initial upward velocity of 5 ft/s at a height of 3000 ft (assuming the air resistance is proportional to its falling speed). The air resists the body's motion with a force of 2 lb for each ft/s of speed. Assuming the constant gravity is 32 ft/s2. 1. find its velocity v = v(t) 2. find its terminal velocity 3. find the distance of falling x = x(t) 4. find the...
57. Find the total derivative dz/dt, given (a) z = x^2− 8xy − y^3 , where...
57. Find the total derivative dz/dt, given (a) z = x^2− 8xy − y^3 , where x = 3t and y = 1 − t. (b) z = f(x, y, t), where x = a + bt, and y = c + k
1.(4 pts) A rectangular tank, shown in Figure A, is 4 ft long, 2 ft wide, and 3 ft high. Initiall...
1.(4 pts) A rectangular tank, shown in Figure A, is 4 ft long, 2 ft wide, and 3 ft high. Initially there is 4 fts of water in the tank and water starts flowing into the tank at the time t Let V (t) denote the volume of the water in the tank at the time t. The graph of V', the derivative of V, o ft3 is given in figure B, where t is in minutes, and V'in min...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the part...
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the particle at time t 4. b) Find all times t in the open interval 0<t <5 at which the particle changes direction. During which time intervals, for 0st s 5, does the particle travel to the left? c) Find...
please help #2(b)) What types of functions are f(x) = e" and g(x) = x". Compare...
please help
#2(b)) What types of functions are f(x) = e" and g(x) = x". Compare the differentiation formulas for f and 9 # 3,4,6,11,14,19.21) Differentiate the function: # 3) f(x) = 186.5 # 4) f(1) = 30 # 6) (t) = {- 36 +t #11) G(x) = VI - 2* # 14) R(r) = YTO #19) y = +*+47 +3 # 21) v = # 25) Find the equation of the tangent line and normal line to the curve...
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx
5. (2 Points) Let -2 -y F (x2+y2+z2)2/3' (2+y2)2/3' (r2+y2+22)2/3 Find the work done by this force field on an F(t) = (1+3t, 1 + 4t2, 1 +5t3) object that moves from (1,1, 1) to (4,5,6) along the curve
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z = 2x2 + 2xy + y2 + 1 at the point P(-1, -3, 18). 2) Find all critical value(s) and classify as maxima/minima/saddle points/none. F(x,y) = 2x + 4y - x2 - y2 - 3 3) Find the directional derivative of z = xy +x in the direction of v= <3,-4> at the point Q(1,4). Also find the direction of maximum increase at this point....
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
3. A 180-Ib person jumps out of an airplane with initial upward velocity of 5 ft/s at a height of 3000 ft (assuming the air resistance is proportional to its falling speed). The air resists the body's motion with a force of 2 lb for each ft/s of speed. Assuming the constant gravity is 32 ft/s2. 1. find its velocity v = v(t) 2. find its terminal velocity 3. find the distance of falling x = x(t) 4. find the...
1.(4 pts) A rectangular tank, shown in Figure A, is 4 ft long, 2 ft wide, and 3 ft high. Initially there is 4 fts of water in the tank and water starts flowing into the tank at the time t Let V (t) denote the volume of the water in the tank at the time t. The graph of V', the derivative of V, o ft3 is given in figure B, where t is in minutes, and V'in min...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the particle at time t 4. b) Find all times t in the open interval 0<t <5 at which the particle changes direction. During which time intervals, for 0st s 5, does the particle travel to the left? c) Find...
please help
#2(b)) What types of functions are f(x) = e" and g(x) = x". Compare the differentiation formulas for f and 9 # 3,4,6,11,14,19.21) Differentiate the function: # 3) f(x) = 186.5 # 4) f(1) = 30 # 6) (t) = {- 36 +t #11) G(x) = VI - 2* # 14) R(r) = YTO #19) y = +*+47 +3 # 21) v = # 25) Find the equation of the tangent line and normal line to the curve...
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