### 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

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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

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=?

F injective iff there exists g such that gf = 1 f surjective iff there exists h such that hf = 1.

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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

If x<-4, f(x) = {[-2(x^3) - 6(x^2) +14x+24] / (x+4)} if x>=-4, f(x) = 5(x^2) +5x+a What value must be chosen for a in order to make this function continuous at -4? Please note the value of a does not equal to 66.

Evaluate the sum (using generating functions) A) 0+3+12+...+3n2. B) 4x3x2x1+5x4x3x2+...+n(n-1)(n-2)(n-3)

(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

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Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y = -x2 + 3x - 3 Here, a = -1, b = 3, c = -3 The axis of symmetry is x = -b/2a = -3 (-2) = 1.5 See attached file for full problem description, equations, charts and diagrams.

Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y = -x2 + 3x - 3

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.)

Problem: Find the vertex and intercepts for y = x^2 + x - 6

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

Consider the function f(x) = 2sinx + e^-x - 1 on the interval r E [?2,2]. If you plot the function, you will see that it has two roots on this interval (a) Write down a first order fixed point method for finding one of the two roots. (b) Will this fixed point method converge for both of the roots (Justify)? If it does not co

Please see the attached file for the fully formatted problem.

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.

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

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,.

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

Differentiation of graphs for Celcius and Farenheit functions

Show all your steps, I need to know what the interpretation is of the symbols. (what does 6, i=3, and xi stand for?).

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)

What are the first four terms of the sequence whose general term is An=4(n-1)!/n! ?

Express the potential function U in cylindrical polar coordinates.. U(x,y,z) = -z(x^2+y^2)^2

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

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)