1. A function f(z) is said to be periodic with a period a, a is not equal to zero. if f(z+ma) =f(z), where m is an integer different from zero. prove that a function, which has two distinct periods say, a and b which are not integer multiples of the other- can not be regular in the entire complex plane. Note: Doubly p
1. A corporation manufactures a product at two locations. The cost of producing x units at a location one and y unites at location two are C1(x)=.01x^2 + 2x + 1000 and C2(y)=.03y^2 + 2y + 300, respectively. If the product sells for $14 per unit, find the quantity that must be produced at each location to maximize the profit P(
Largest rectangle between two plots. See attached file for full problem description.
1. Sketch Graph: f(x) = 3x4-2x³-12x²+18x (MUST SHOW ALL WORK) 2. Sketch Graph: f(x) = x4-18x²+81 (MUST SHOW ALL WORK) Note: The 4 in both problems is an exponent
I need help doing two calculus problems #11, and #13. Each one is 5 parts (a,b,c,d,e) I have attached 3 files a) class notes for rectilinear motion b) the assignment (only problems 11 and 13) and my initial work on #11. I understand how to calculate 11 a, b, c but I get stuck on d, e. Can you explain what is going on and d
Suppose that y1, y2 are linearly independent solutions to the differential equation: a2 (x) y'' + a1 (x) y' + a0 (x) y = 0. a) Show that a2 (y1 y2'' - y2 y1'') + a1(y1 y2' - y1' y2) = 0 b) show that (a) implies a2 W' + a1 W = 0 {here W means the Wronskian) c) show that the equation in (b) implies W
3. Write the first four terms of the defined sequence a lower case 1 = 1 a lower case n=na lower case n-1, n>1 9. Write the following in summation notation 3+6+9+12+15 10. Write the following in summation notation: x+x^2/2 + x^3/6 + x^4/24 14. Find the fifth term in the expansion of (a + b)^16 15. Write the bi
Use a power series method to find the solution of x^2 y'' + 2xy' + 4y = 0 that is valid in any interval not including the singular point. y=0 is a trivial solution which exists for any linear Homogeneous equation. So it is correct but absolutely not enough to complete the problem. Since the equation is linear and has non
A relation between a function f(x) and its derivative f'(x) = x√f(x) is given with an initial condition on f(x) as f(4)=16. One needs to find the value of the second derivative of the function i.e., f"(4). Also an expression to f(x) in terms of x is to be evaluated. Please see the attached file for the fully formatted
Sketch the following function f(x) = -x³ + 3x² + 9x +5
Consider the differential equation (dy/dx) = (-xy^2)/2. Let y=f(x) be the particular solution to this differential equaiton with the initial condition f(-1)=2. a) On the axis provided sketch a slope field for the given differential equation t the twelve points indicated. (the x-axis goes from -1 to 2 and the y-axis goes from
Does the series a_n defined by the formula below converge or diverge? Give reason for your answer. a_1 =3 a_(n+1) =( n / n + 1)(a_n)
(See attached file for full problem description)
Laplace Transforms. See attached file for full problem description.
Let f and g be the functions given by f(x) = ¼ + sin(Pi*x) and g(x) = 4^ -x. Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let S be the shaded region in the first quadrant enclosed by the graphs of f and g. a) Find the area of R. b) Find the areas of S. c) Find t
Using maple 10: Given the curve: f(x,y)=12+10y-2x^2-8xy-y^4 a. Find the critical points correct to 3 decimal places b. Classify the critical Points cf. Generate and graph; identify the highest point on the graph
Using maple 10 do the following: a. Using a graph(s) estimate the local max., min., and saddlepoints of f(x,y)=x^3-3x+y^4-2y^2 b. Again using Maple use calculus to find these values exactly
Please explain in as much detail as possible finding an equation in standard form for each conic. 1) Parabola, focus (-4,0), directrix X=2 2) Hyperbola, foci (0, +/_3), vertices (0,+/-1) 3) Ellipse, center (2,2), a focus (0,2), vertex (5,2)
(See attached file for full problem description) --- 10. y = √x + 3 (√x+3 is all squared). Please use the Chain Rule 16. f (w) = w √w + w² (√w is only squared) Please use the Chain Rule 18. y = 4x³ - 8x² Please use the Chain Rule 5x 46. Margi
Water is pumped_into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate of √(t+1) gallons per minute for 0 ≤ r ≤ 120 minutes. At time t = 0, the tank contains 30 gallons water. (a) How many gallons of water leak out of the tank from time r = 0 to r = 3 minut
See the attached file. 4. Let h(x) be a function defined for all ... such that h(4) = ?3 and the derivative of h(x) is given by .... (a) Find all values of x for which the graph of Ii has a horizontal tangent, arid determine whether 1 has a local maximum, a local minimum, or neither at each of these values. Justify your answer
The plane 4x-3y+8z=5 intersects the cone Z^2=x^2 + y^2 in an ellipse a. Graph the plane, cone and ellipse b. Use Lagrange multipliers to find the highest and lowest points on the ellipse. This problem must be solved using maple 10 (or 9) please show all work and data entries and outputs.
The problem is: ∫∫ y/[x^2 + y^2] dA R R is the triangle bounded by y=x, y=2x, x=2
1.) Determine lim An= (n^2-11n+22)/(3n^2+29n+19) 2.) Sketch graph 2x^2-4x+y^2+4y=10.
Prove that if Series An (small "a", sub "n") is a conditionally convergent series and r is any real number, then there is a rearrangement of Series An whose sum is r. [Hints: Use the notation of Exercise 39 (I'll show below). Take just enough positive terms An+ so that their sum is greater than r. Then add just enough negati
1. DERIVE EQUATION 6-15 2. DERIVE EQUATION 6-48 AND 6-54 3. SOLVE ALL PROBLEMS SHOWN BELOW: 67. Water at 20°C flows through a smooth pipe of diameter 3 cm at 30 m3/h. Assuming developed flow, estimate (a) the wall shear stress (in Pa), (b) the pressure drop (in Pa/rn), and (c) the centerline velocity in the pipe. What is the
(See attached file for full problem description) --- 1) Consider the following function: a) f (x) = 9x2 - x3 b) f (x) = x + 1 x - 2 c) f (x) = x2/3 (x - 5) for each of the above functions complete the following table. Show the work to justify your answers below the table. f(x) is i
Using the given parameters, find the equation for the plane. Please show all work and a diagram if possible. Thank you. The plane through (1, -1. 3) parallel to the plane 3x + y + z = 7
In a backyard, there are two trees located at grid points A(-2,3) and B(4,-6). a) The family dog is walking through the backyard so that it is at all times twice as far From A as it is from B. Find the equation of the locus of the dog. Draw a graph that shows the two trees, the path of the dog. and the ralationship defining
6) If a nation's consumption function is given by : C(I) = 0.3I + 0.8 √I + 6 where I is national income, measured in billions of dollars a) Find the nation's marginal propensity to consume b) Find the nation's marginal propensity to save c) Evaluate the marginal propensity to save when I = 64