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MATH 16A WORKSHEET 10-
(1) Suppose x and y are both differentiable functions of t and are related by the equation y4 - x2 = 1. Use implicit differentiation with respect to t to determine dy/dt in terms of x, y, dx/dt .
(2) A tank has the shape of an upside down cone with radius 3 meters and height 4 meters. Water is pouring into the tank at 2 cubic meters per second. How fast is the water level rising when the water level is 3 meters high?
(3) Solve the equation 22x - 2x+2 - 32 = 0 for x.
(4) Find f' and f'' for f(x) = ex2-x. Find the absolute minimum and explain why it is an absolute minimum.
(5) Find the derivative of the following functions.
(a) f(x) = ln √x
(b) f(t) = (ln(e2t + 1))2
(c) f(x) = ln(x ln(x + 1)).
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f(x, y, z) = x3 + x2y2z2 +z3. Find directional derivative at (1,1,1) along (1,0,1). Find direction in which Du f(x,y,z) is maximal. What is the value of Dmax f(x,y,z).
The profit of each bookcase is 40$ and each desk is 75$. How many of each product should be made each month in order to maximize profit.
Find the domain and range of these functions
determine the limit of the sequence or show that the sequence diverges by using the appropriate Limit Laws or theorems.
The polynomial 0.041h-0.018a-2.69 can be used to estimate the lung capacity,in liters,of a female with height H,in centimeters,and age a,in years
Find each of the following for the given inner product defined in R^2 =3u(subscript 1)v(subscript 1) + u(subscript 2)v(subscript 2)
When a ball is thrown, its height in meters after seconds is given by the equation, where is the initial upwards velocity in meters per second
A copier that originally cost $300 was sold on the installment plan as $28 per month for 12 months. Find the installment price if no down payment was made. Find the finance charge.
ace truck rental charges 54.00 a day plus 9 cent per mile. ronis truck rental charges 38.00 a day plus 13 cent per
verify that E is a constant of motion for the system of the first two equations and find the equilibria of the system of the first two equations
Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line. 5x-6y-12=0
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