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Graphs and Functions

What are all the intercepts of the graph of...? (6 Problems)

20. At what points does the graph of y = x^2 - 3x -10 cross the x-axis 21. What are all of the intercepts of the graph of y = 15x^2 + 89x - 6? 22. What are all the intercepts of the graph of y = 2x^2 - 11x + 5? 23. What are all the intercepts of the graph of y = 6x^2 + 13x + 6? 24. What are all the

Tarea de clase

(See attached file for full problem description with equations) --- 1.- Let , . Does is uniformly converge on (-1,1)? --- We use the book Methods of Real Analysis by Richard Goldberg.

Functions

Please show details of how to arrive at the solutions so I can understand how to do similar problems. (See attached file for full problem description with equations) --- (1) Given that the polynomial function has the given zero, find the other zeros. (2) Find the horizontal asymptote, if any, of the rational function.

Functions And Notation

1. From the function f (x)=IxI How would I go about finding its image set using interval notation? 2. Again using interval notation, how would I go about finding the image set of the graph g(x)= Ix+3I -2 ? And how then would I go on to solve the equation g(x)=1, and discover if it had any geometrical significance? 3. How

Lines and Circles

Say I have for example a circle with centre C(7,-5) passing through point A(6,-3) (With tangent line and radius, AC, being perpendicular.) 1. How would I go about finding the gradient of the tangent? 2. How would I go about finding that the equation of the tangent at A is the line x=2y+12 ? 3. And how would I go about find

Root

(See attached file for full problem description with equation) --- Solve this problem. Explain why has a root, and indicate an interval where this root lies. ---

Differentiation

Please sketch a graph of an arbitrary function f that satisfies the given condition but does not satisfy the conditions of the Mean Value Theorem on the interval [-5,5] f is not continuous on [-5,5]. Please offer as much explanation as practicable.

Graphing

Graph f(x) = 5x^2 / (x^2) + 2 I need to know the x and y intercepts and all known asymptotes

Find maximum subject to constraint and use result in proof

(See attached file for full problem description with equations) --- Find the maximum value of the function subject to the constraint . Use the result to prove that Use a similar method to prove that for any positive numbers ,... ---

What is the expected yield on notes from year 1 to 2, assuming the PEH holds? If inflation for the next year is expected to be 4.5%, what would the expected real rate of interest be on the 3-month T-bill? Plot the yield curve for these Treasury securities. Using the three theories we have discussed, explain how each one helps explain the shape of this yield curve.

1. If U.S. Treasury yields are as follows: 3 month 6.0% 6 month 6.3% 1 year 6.5% 2 year 6.6% 5 year 6.4% 10 year 7.5% 30 year 8.0% a. What is the expected yield on notes from year 1 to 2, assuming the PEH holds? b. What is the expected yield on notes from year 2 to 5, assuming th

Algebra Review

(See attached file for full problem description with equations and diagrams) --- 1. Simplification of linear algebraic expressions and expressions with fractional coefficients and solve x; 2. Solving simple linear equations with fractional coefficient: 3. Solving inequalities with fractional coefficient: 4.

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=?