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- [Solution] Find the total differential z=(x^2)/(y) #11100
- Solution: Find the total differential w=x^2yz^2+ sin yz #11101
- (See Solution) Let f(x,y)=x{e^y} (a) Evaluate f(1,2) and f(1.05,2.1) and calculate Δ z (b) Use the tot #11102
- [Solved] The centripetal acceleration of a particle moving in a circle is a=({v^2})/(r), where v is the veloc #11103
- [Solution] Compute (dw)/(dt) using the Chain rule: w=√{x^2+y^2} x= cos t, y={e^t} #11104
- [Solution] For w= cos (x-y) , x={t^2},y=1 , (a) Compute (dw)/(dt) using the Chain rule #11105
- [Solution] Find (∂ w)/(∂ s) and (∂ w)/(partial t) at the given points w=y^3-3x^2y #11106
- [Solved] Find (∂ w)/(∂ s) and (∂ w)/(partial t) at the given points w= sin (2x+3y) #11107
- [Solution] Find (∂ w)/(∂ r) and (∂ w)/(partial θ ), for w=√{25-5x^2-5y^2} and #11108
- Solution: Differentiate implicitly to find the first derivatives xz+yz+xy=0 #11109
- [Solution] Find the directional derivative at the point P and direction v f(x,y)=x^3-y^3, P(4,3), v=(&ra #11110
- (See Solution) Find the directional derivative at the point P and direction v f(x,y)= arccos xy, P(1,0), v= #11111
- [Solution] Find the directional derivative at the point P and direction v f(x,y)=x^2+y^2+z^2, P(1,2,-1) #11112
- [Solved] Find the directional derivative at the point P and direction Q f(x,y)= cos (x+y), P(0,π) #11113
- [Solved] Find the gradient of the function, and the maximum value of the directional derivative f(x,y)=y #11114
- [Solved] Find the gradient of the function, and the maximum value of the directional derivative w(x,y,z)= #11116
- [Solution] Identify any extrema of the function by recognizing its given form or after completing the square. V #11117
- [Solved] Identify any extrema of the function by recognizing its given form or after completing the square. V #11118
- (See Solution) Examine the function for relative extrema f(x,y)=x^2+6xy+10y^2-4y+4 #11119
- (Solved) Find the critical points and test for relative4 extrema. List the critical points for which the Seco #11120
- [Solved] Find the absolute extrema of the function over region R. f(x,y)={{(2x-y)}^2} R: The triangular #11121
- [Solution] Find the absolute extrema of the function over region R. f(x,y)=x^2+2xy+y^2 R={ (x,y): |x|≤ 2 #11122
- [Solved] Find 3 numbers x, y and z that satisfy the given conditions: The sum is 32 and P=xy^2z. #11123
- [Solved] Find 3 positive numbers x, y and z that satisfy the given conditions: The sum is1 and the sum of the #11124
- [Solved] The material for constructing the base of an open box costs 1.5 times as much as per unit of area as #11125
- (See Solution) Identify the constraint and level curves of the objective function. Use Lagrange multipliers to find #11126
- [Solved] Use Lagrange multipliers to find the indicated extrema Minimize f(x,y)=3x+y+10 #11127
- [Solution] Use Lagrange multipliers to find the indicated extrema Minimize f(x,y)=√{x^2+y^ #11128
- [Solved] Use Lagrange multipliers to find the indicated extrema Maximize f(x,y,z)=xyz #11129
- [Solution] Use Lagrange multipliers to find the indicated extrema Maximize f(x,y,z)=x^2+y^2+z^2 #11130
- [Solution] Use Lagrange multipliers to find the indicated extrema Maximize f(x,y,z)=xyz #11131
- [Solved] Use Lagrange Multipliers to find the minimum distance from the curve to the indicated point: {{( #11132
- (See Solution) Solve Max V=xyz , s.t. 1.5xy+2xz+2yz=C #11133
- [Solved] Let T(x,y,z)=100+x^2+y^2 represents the temperature at each point on the sphere x^2+y^2+z^2=50. Find #11134
- [Solved] Find the interval of convergence of the power series. Also check at the end points of the interval #11141
- [Solution] Find the interval of convergence of the power series. Also check at the end points of the interval #11142
- [Solution] Find the interval of convergence of the power series. Also check at the end points of the interval #11143
- (Solved) Find the interval of convergence of (a) f(x) (b) f'(x) (c) f''(x) (d) ∫{f(x)dx} Also check #11144
- (See Solution) Let f(x)=∑limits_{n=0}^{∞ }{({{x}^n})/(n!)} (a) Find the interval of convergence of f. (b #11145
- (Solved) Find a power series centered at c and determine the interval of convergence. f(x)=(4)/(5-x), c=-2 #11146
- [Solved] Find a power series centered at c and determine the interval of convergence. f(x)=(3)/(2x-1), c=2 #11147
- Solution: Find a power series centered at c and determine the interval of convergence. f(x)=(4)/(3x+2), c=2 #11148
- (See Solution) Find a power series centered at c and determine the interval of convergence. f(x)=(4)/(4+x^2), c=0 #11149
- [Solution] Find a power series centered at c and determine the interval of convergence. h(x)=(x)/(x^2-1)=(1)/( #11150
- Solution: Find a power series centered at c and determine the interval of convergence. f(x)=(2)/({{(x+1))^3}} #11151
- [Solved] Find a power series centered at c and determine the interval of convergence. f(x)=ln (x^2+1) #11152
- (Solved) Find a power series centered at c and determine the interval of convergence. f(x)= arctan (2x) #11153
- (Solved) Find and simplify the function values f(x,y)=4-x^2-4y^2 (a) (0, 0) (b) (0, 1) (c) (2, 3) (d) ( #11154
- Solution: Find and simplify the function values f(x,y,z)=√{x+y+z} (a) (0, 5, 4) (b) (6, 8, -3) (c) #11155
- Solution: Find and simplify the function values g(x,y)=∫_{x}^y{(1)/(t)dt} (a) (4, 1) (b) (6, 3) (c) #11156
- (Solved) Sketch the surface given by the function. f(x,y)=6-2x-3y #11160
- [Solved] Sketch the surface given by the function. z=1/2√{x^2+y^2} #11161
- [Solved] Describe the level curves of the function. Sketch the graph of the level curves for the given value #11162
- (Solved) Describe the level curves of the function. Sketch the graph of the level curves for the given value #11163
- [Solved] Sketch the graph of the level surface f(x,y,z)=c at the given value of c. f(x,y,z)=4x+y+2z, c= #11164
- [Solution] Sketch the graph of the level surface f(x,y,z)=c at the given value of c. f(x,y,z)=x^2+1/4y^2-z #11165
- (See Solution) Find the limit and discuss the continuity of the function {(x,y)→ (1,1)} lim (xy)/(x^2+y^2) #11167
- (See Solution) Discuss the continuity of the function and evaluate the limit of f(x,y) as (x,y)→ (0,0) f( #11168
- (See Solution) Discuss the continuity of the function and evaluate the limit of f(x,y) as (x,y)→ (0,0) f( #11169
- [Solution] Find each limit (a) {Delta x→ 0} lim (f(x+Δ x,y)-f(x,y))/(Delta x) (b) {Delta x→ 0}l #11172
- Solution: Find the time required for a $1,000 investment to triple when the interest rate, r, equals 0.085, co #11215
- [Solution] A silo is to hold 10,000 cubic feet of grain. The silo will be cylindrical in shape and #11247
- [Solved] Tank is 10 ft in diameter and 15 ft long. Density of gasoline is 45 lb/ft3. The filter cap of each c #11265
- [Solution] A kite is flying 500 ft above the ground. The string weighs 1/16 oz per foot and is stretched in a s #11266
- Solution: Surface area rotating R around x-axis f(x)=x^3, g(x)=10-x, and the x-axis. #11267
- (See Solution) Find all critical numbers for the function f(x)=x+(36)/(x). #11290
- (See Solution) Find all open intervals on which the function f(x)=√[3]{x^2-1} is decreasing. #11291
- Solution: Find the point(s) of relative extrema for the graph of the function f(x)=x{{(x-4)}^3} #11292
- [Solution] Find all intervals on which y=(4x^2-x)/(x^4) is concave up. #11293
- [Solution] Let f(x)=x^3-x^2+3. Use the Second-Derivative Test to determine which critical numbers, if any, give #11294
- [Solution] Find all horizontal and vertical asymptotes for the graph of the function f(x)=(6x^2)/(8-x^3) #11297
- [Solved] Determine where the graph of y=x(x^2-12) is increasing and decreasing, if it has any relative extrem #11298
- [Solved] Use the techniques learned in this chapter to sketch a graph of f(x)=(1)/(x^3) #11299
- [Solved] Find all inflection points for the graph of the function f(x)=x^4-4x^3+16x+8 #11300
- (See Solution) Find the x-coordinate of the point of diminishing returns for the revenue function R(x)=(300x^2- #11303
- (See Solution) In a complete sentence, explain what must be true for a function y = f(x) to have a maximum point at #11305
- [Solved] Find the following indefinite integral ∫{3{t^4}dt} #11306
- (Solved) Find the following indefinite integral ∫{4{{y}^{-3}}dy} #11307
- (Solved) Find the following indefinite integral ∫{{{(x^2-1)}^3}(2x)dx} #11308
- (Solved) Find the following indefinite integral ∫{u^3√{u^4+2}dx} #11309
- (Solved) Find the following indefinite integral ∫{(t+2{t^2})/(√{t)}dt} #11310
- (Solved) Find the following indefinite integral ∫{(5)/(2x-1)dx} #11311
- [Solution] Find the following indefinite integral ∫{(x^2)/(3-x^3)dx} #11312
- [Solved] Find the following indefinite integral ∫{(1)/(√{x+1)}dx} #11313
- [Solved] Find the following indefinite integral ∫{(5{e^{-2x}}+1)dx} #11314
- [Solution] Find the following indefinite integral ∫{(3)/(1+{e^{-3x)}}dx} #11315
- Solution: Find the area of the region defined by the curves: f(x)=x^2+2x+1 , g(x)=2x+5 #11316
- [Solution] Find the area of the region defined by the curves: f(x)={{(x-1)}^3} , g(x)=x-1 #11317
- [Solution] Find the area of the region defined by y=({e^{1/x}})/(x^2),y=0,x=1,x=3 #11318
- Solution: I need to find the volume of the largest right circular cylinder, which can be transcribed inside a #11351
- (Solved) Find the value of at t = 0 if and #11384
- (Solved) Are there any points on the curve where the slope is -3/2? If so find them. #11385
- (Solved) What are the maximum and minimum values of the function on the interval - . Notice that the interva #11386
- [Solution] Show the equation has exactly one solution . #11387
- Solution: Given the first derivative of a function y = f(x). i. At what points, if any, does the graph of f h #11388
- [Solution] A customer has asked you to design an open-top rectangular stainless steel vat. It is to have a squa #11389
- (See Solution) Find the linearizations of a. b. #11390
- [Solved] Find the total area of the region between the graph of f and the x-axis. #11392
- [Solution] Find the total area of the region between the graph of f and the x-axis. #11393
- (Solved) Let R be the region in the upper half-plane bounded by the circles x^2 + y2 = 1 and x^2 + #11431
- Solution: Let R be the region in three dimensional which lies in the first octant and is bounded by xz-coordin #11432
- [Solution] Let D be the solid bounded below by the cone z=2√{x^2+y^2} and above by the plane #11433
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