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Graphs and Functions


F(x) = 4sinx / (2sinx+4cosx) the equation of the tangent line to f(x) at a=0 is y=sx+b Find: y=sx+b

Parabola and tangent lines

The parabola y= x^2+4 has two tangents which pass through the point (0,-2). One is tangent to the parabola at (a, a^2+4) and the other at (-a, a^2+4) where a is a certain positive number. The question is a=?

Solve Finite Difference Equation

See attached file for full problem description with equation. --- Find analytically the solution of this difference equation with the given initial values: Without computing the solution recursively, predict whether such a computation would be stable. (Note: A numerical process is unstable if small errors made at one

Evaluate graphs of derivative functions

(a) Suppose the graph in Figure 4.1.78 is that of a function g(x). Sketch the graph of the derivative g; (b) On the other hand, suppose the graph above is that of the derivative of a function f. For the interval ..., tell where the function f is (i) increasing; (ii) decreasing. (iii) Tell whether f has any extrema, and if so

Find Domain, Graph, Height, Minimum Surface Area of a Box Given its Volume

Consider an open-top box with a square base and a volume of 108 cubic inches. Let x be the length of a side of the base. a) Calculate the height h as a function of x. Is this function even, odd, or neither? b) What is the domain of the function above? (Note that there may be physical and/or mathematical restrictions.)

Uniform Convergence of Sequnece

Prove : Let f1,f2.... be a sequence of continuous functions convergent uniformly on a bounded closed interval [a,b] and let c E[a,b] . For n = 1,2,...., define ..... Then the sequence g1,g2.... converges uniformly on [a,b]. Is the same true if [a,b] is replaced by ? Please see the attached file for the fully formatte

Three-dimensional graphing

1. Find the distance from the origin to the line passing through the point P(3,1,5) and having the direction vector v=2i-j+k. 2. Graph z=x^2 in space.

Graphing to check answers

Using graphing to check your answers is helpful. When you factor a trinomial into two binomials, each binomial represents a linear relationship. If you plot the two binomials (which are just lines) on a graph, what do they have in common with a plot of the trinomial itself? More important than that, how can this information be u

Measurable Functions

Suppose u(x) : X--> R v(x) : X --> R Both u(x) and v(x) are measurable Let f(x) : x --> R^2 f(x) = (u(x), v(x) ) Then f (x) is measurable Now prove a generalization of the above. That is, prove: if u_1(x) : X--> R u_2(x): X--> R . . . . u_n(x) : X--> R u_1,.

Graph, Solve for x and Inverses

1. Graph for the function: f(x)=2-4^x 2. Solve for x: ln(7x-1)=6 3. Solve for x: lnx=3+ln(x-1) 4. Are the following funtions inverses of each other? 1. f(x)=x-1/3 g(x)=3x-1

Functions : L-Spaces ( Lebesgue Spaces )

Consider the following function: f(x) = 1/x for x in [1, infinity) = 1 for x in (-1,1) = -1/x for x in (-infinity, -1] Please explain why f(x) is in L^2(R)L^1(R)

Spherical polar coordinates

I have an answer for this problem, so it is just a check and confirmation I require. --- (See attached file for full problem description)

Carmichael number

Which one of the following is true A Carmichael number is: a) a 2 pseudo-prime b) a 3 pseudo-prime c) a 5 pseudo-prime d) All of the above e) None of the above f) Just (a) and (b)