6. The gradient of a function g(x, y, z) at the point (-3,4,5) is (-2, 1, 2). (a) Find the values of the partial derivatives gx, gy, and gz at the point (-3,4, 5). (b) Find the maximum rate of change of g at the point (-3, 4, 5) and.
A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 1000 bacteria in the initial polulation and the number doubled after the first 30 minutes, how many.
A) Plot the curve corresponding to y =2x2 +3 and find the slope at x = 3 by graphical means.
B)Find the area under the curve between x = 0 and x = 3.
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82 3 Evaluate d2, where Cis the "figure eight" contour shown below (first C 24 2 express C as the union of two simple closed curves C1 and C2. Pay close attention to the orientation of these curves).
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A bookstore can obtain the best-seller 20,000 Leagues Under the Majors from the publisher at a cost of $6 per book. The store has been offering the book at a price of $30 per copy and has been selling 200 copies per month at this price. The bookstore is planning.
6. What can you say about a function f based on the information that f is... a. zero at a given point b. negative over a given interval? c. positive over a given interval? 7. Complete Summary Box D3.2 by filling in the blanks with increasing or decreasing, as appropriate..
A car moves along a straight road in such a way that its velocity (in feet per second) at any timet(in seconds) is given by
Find the distance traveled by the car in the7sec fromt= 0 tot=7..
A 840 gallon pool stores water for irrigation. The water is contaminated by a toxic substance at a concentration of 80 ppm (parts per million). A filter is installed that can remove 70% of the toxin. It can filter 10 gallons per minute. The filtered water is returned to the.
8. If yr (ar) is a solution of the DE a(z)y" b(r)y' c(r)y 0 and y (T) 0, then use the Abel's formula to derive that b(z) dar is also a solution of this DE. (This provides a different approach from the method of reduction of order to seeking the.
6. Suppose f(x) = 1.5x^2 for - 1 < x < 1 and f(x) = 0 otherwise. Determine the following probabilities: a. P(-0.5 X 0.5) b. P(X < -2) c. Determine x such P( x < X) = 0.05
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7. For the function f (r) whose values are given in the table below, approximate f(z) dz using the Midpoint Rule with 2 subintervals. O 1.2 4.3 6.5 1 A. 15.4 B. 12.5 C. 12 D. 16.7 E. 13
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6)Given r(x) = x^2-4x-5/x-3
a) Find the x-intercept(s)
b) Find the y-intercept.
c) Find the asymptotes. Label the asymptotes as vertical, horizontal or slant asymptote.
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A confined aquifer with a horizontal bed has a varying thickness. The aquifer is inhomogeneous with K = 12+0.006x, where x =0 at point 1, and the piezometric heads at point 1 and 2 are 14.2 m and 18.8 m, respectively measured above the upper confining layer. Assuming the flow.
A 1 l-Ohm resistor and a variable resistor of resistance R are placed in parallel. The expression for the resulting resistance RT is given by RT =11R/11+R. Determine the limiting value of RT as R rightarrow infinity. The limiting value of RT is . (Simplify your answer.) Enter your answer.
(6 points) Consider the function y 2x3 0.4x 8. a. What is the slope of this function when x 0.2? b. hat is the second-order derivative of y when x 0.2? c. Is y convex or concave when x 0.2?
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7- -12 points LarCalcET6 4.8.006. My Notes Ask Your Teacher Find the tangent line approximation Tto the graph of f at the given point. Use this near approximation to complete the table. (Round your answers to four decimal places.) f(x) og x, (7, 1) 7 7.01 6.9 7.1 f(x) T(x).
7. Find the exact length of the polar curve described by: (see image)
Find the exact length of the polar curve described by: r = 10e^-theta on the interval 3/2 pi lessthanorequalto theta lessthanorequalto 9 pi.
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A campus has 5000 students. After the Christmas break one student returns carrying a flu virus. Assume that the rate at which the virus spreads is proportional to the number of infected students P(t), but also to the number 5000?P(t) of students not yet infected. Here time is measured in.
A child wanders slowly down a circular staircase from the top of a tower. With X, y, z in feet and the origin at the base of the tower, her position t minutes from the start is given by x = 25 cos t, y = 25 sin t, z.
A 18 ft ladder leans against a wall. The bottom of the ladder is 5 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec. Find the velocity of the top of the ladder at time t=1. The velocity of ladder at.
6. Solve the given differential equation 8xdx + dy = 0
y = ________?
(Simplify your answer. Use C as arbitrary constant)
7. Solve the given differential equation
\(x^{2} + (x^{3} - 3) y ' = 0\)
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9. For the following applied max/min question, onlyformalize the problem (.e. indicate constraint equation (s) and objective equations), first setting up the parameters: rectangular yard, adjacent to a river "A farmer wants to fence 3 sides of a bank (see the picture). The opposite to the bank is to be.
A) The region bounded by the graph of y = 1/x^2, the line x=1 and the x-axis is rotated around the line y = -3. What is the volume of the resulting "infinite funnel"? B) If the same region is rotated around the y-axis, what is the volume of the.
6)
(a) Simplify the expression cos(arctan(x)).
(b)Evaluate arccos cos(2pi).
7) State the domains of the following functions:
(a) ln(lnx)
(b)arctan(1/x)
(c) \(arcsing(x^2-1)\)
(d) f'(x), where \(f(x)=\sqrt{|x|} \) (that is,.
(6) Consider the Lotka Volterra system In terms of the parameters a B, m, compute the two equilibrium points of this system. Com- pute also the derivative of v at each of the two fixed points and find their eigenvalues. Then, discuss: is it reasonable to expect periodic solutions to.
6. Find the equation of the tangent line to the graph of the function f(x)= x root 2x^2+7 at the point(1,3). Please explain mistake and correct form. Based from Apllied calculus Tan 9th. Thanks.
A balloon is at a height of 40 meters, and is rising at the constant rate of 5 m/sec. A bicyclist passes beneath it, traveling in a straight line at the constant speed of 10 m/sec. How fast is the distance between the bicyclist and the balloon increasing 2 seconds.
A : Integers greater than 10.
B: Odd negative integers.
C: Integers with absolute values less than 100,000.
D: Real numbers between 0 and 2
E: The set {2,3} x Z+
F: Integers that are.
A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls.
^125 I has a half-life time of 60 days. The purchase price of the source is composed of a fixed cost of $300 and a cost per mCi activity of $1 The source provides 100 counts/s/mCi. The minimum acceptably count rate is 30,000/s. How much do I have to pay.
60. TRUE OR FALSE If f(x) has a vertical asymptote at x = c, then either lim x tends to e^x f(x) = lim x tends to e^x = + infinity or lim x tends to e^x f(x) = lim x tends to e^x f(x) = - infinity. Justify your.
