Tutors Answer Your Questions about Complex Numbers (FREE)
Question 1026908: The function C(t) = K(e^(-at) - e^(-bt)), where a,b,K are positive constants and b>a, is used to model the concentration at time t of a drug injected into the bloodstream.
a.Find the limit of C(t) as t approaches infinity.
b.Find dC/dt, the rate of change of drug concentration in the blood.
Click here to see answer by robertb(5830)   |
Question 1027086: Is there a faster method to factorise the equation x^3 - 2(1+i)x^2 + 3ix + (1-i) = 0, I used the factor theorem to find one factor then long division to find the others, however it was a very long process so I was wondering if there is a quicker method? Thanks
Click here to see answer by robertb(5830) |
Question 1027256: Provide an example of functions f(x) and g(x) with the limit as x approaches infinity of f(x) is infinity and the limit as x approaches infinity of g(x) is infinity such that:
A) The limit as x approaches infinity of f(x)/g(x) is infinity.
B) The limit as x approaches infinity of f(x)/g(x) is 6.
C) The limit as x approaches infinity of f(x)/g(x) is zero.
D) Is it possible to have the limit as x approaches infinity of f(x)/g(x) is -1? explain.
Click here to see answer by richard1234(7193)  |
Question 1027265: X | f(x) | g(x) | df/dx | dg/dx
_____________________________
-2 | 3 | 1 | -5 | 8
-1 | -9 | 7 | 4 | 1
0 | 5 | 9 | 9 | -3
1 | 3 | -1 | 2 | 6
2 | -5 | 3 | 8 | 0
Using the table of data:
a) Let j(x) = f(x) g(x) sinx. What is dj/dx when x =0?
b) Let h(x) = [f(x) + x^2]^3. What is dh/dx when x=1?
c) Let k(x) = (ln(x+2))/g(x). What is dk/dx when x = -1?
Provide a graph for each f(x) and g(x).
Click here to see answer by robertb(5830) |
Question 1027573: Let f be a function such that f(0) = 2 and f'(x)<=6 for -10<=x<=10.
A) What is the maximum possible value of f(4)?
B) What is the maximum possible value of f(2)?
C) Can f(5) be negative? Can f(5) = 0? Why or Why not?
D) Can f(5) = 31? Can f(5) = 35? Why or why not?
Click here to see answer by robertb(5830) |
Question 1027568: Let f(x) an always positive function such that du/dx < 0 for all real numbers.
A) Let h(x) = [f(x)]^2. For what values of x will h(x) be increasing.
B) Let j(x) = f(f(x)). For what values of x will j(x) be increasing.
Click here to see answer by robertb(5830) |
Question 1027572: Let f be a function such that f(0) = 2 and f'(x)<=6 for -10<=x<=10.
A) What is the maximum possible value of f(4)?
B) What is the maximum possible value of f(2)?
C) Can f(5) be negative? Can f(5) = 0? Why or Why not?
D) Can f(5) = 31? Can f(5) = 35? Why or why not?
Click here to see answer by Fombitz(32388)  |
Question 1027567: A flexible chain hangs from the tops of two poles of equal length whose bases are at x = +-L. The height of of the chain above the ground (y=0) is given by y=acosh(x/a).
A) If the poles are 4m high, find L.
B) The lowest point of the chain is at x=0, where the chain is 2m above the ground. Find a.
C) Provide a graph for the resulting catenary.
Click here to see answer by Fombitz(32388) |
Question 1027563: Suppose that your foot length L in inches is related to your height h in inches by L = (4/3)sqrt(h). In one (non-leap) year you have a growth spurt in which you grow from 64 inches to 69 inches. Assume that your height changes at a constant rate throughout the year.
A) Find an expression for dL/dt.
B) What was the fastest rate of growth that your foot experienced during this time? When did it occur?
Click here to see answer by rothauserc(4718)  |
Question 1027710: Consider this function f(x) = x^3+ax^2+bx+c where a>=0, b>0
Over what intervals is f concave up? Concave down?
Show that f must have one inflection point.
Given that (0,-2) is the inflection point of f, solve for a and c and then show that f has no critical points.
Click here to see answer by robertb(5830) |
Question 1027711: Consider this function g(x) = (c(1-x^2))^1/2 where c is not 0.
A)Graph some of these curves of different negative values of c. Provide sketches for each curve and describe in words what these curves look like for different negative values of c.
B)Graph some of these curves of different positive values of c. Provide sketches for each curve and describe in words what these curves look like for different positive values of c.
Click here to see answer by KMST(5328)  |
Question 1027652: Let f(x) be sqrt(3-x) where x <= 1, x^2 where 1= 3.
Find:
limit of f(x) as x approaches 1-
limit of f(x) as x approaches 1+
limit of f(x) as x approaches 1
limit of f(x) as x approaches 3-
limit of f(x) as x approaches 3+
limit of f(x) as x approaches 3
limit of f(x) as x approaches 9
limit of f(x) as x approaches -6
Where is f discontinuous?
Click here to see answer by Fombitz(32388) |
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