Evaluate the contour integral of z^2/(4-z^2) around the circle |z+1|=2. The question is attached in correct mathematical notation, along with the student's (incorrect) initial attempt. You will need to refer to this initial attempt when reading the solution.
A 10-ft trough filled with water has a semicircular cross section of diameter 4 ft. How much work is done in pumping all the water over the edge of the trough? Assume that the water weighs 62.5lb/ft^3.
3. Solve the wave equation, ∂2u/∂t2 = c2(∂2u/∂x) -∞ < x < ∞ With initial conditions, u(x,0) = (1/x2+1)sin(x), and ∂u/∂t(x,0) = x/(x2+1) 4. Suppose that f is a 2п-periodic differentiable function with Fouier coefficients a0, an and bn. Consider the Fourier coeffici
1. Evaluate: ∫2cos2 xdx 2. Figure 12.1 y = 9-x2 , y=5-3x Sketch the region bounded by the graphs of Figure 12.1, and then find its area. 3. Figure 13.1 1?0x4dx Approximate the integral (Figure 13.1); n=6, by: a) first applying Simpsonfs Rule and b) then applying the trapezoidal rule. 4. Find
1)Figure 11.1: 0<=x<=(pie)/2 R is bounded below by the x-axis and above by the curve y = 2cos(x), Figure 11.1. Find the volume of the solid generated by revolving R around the y-axis by the method of cylindrical shells. 2)Figure 15.1: y= 1/(x^2+4x+5) R is the region that lies between the curve (Figure 15.1) and t
See attachment and show work. 1. Find a function f(x) = x^k and a function g such that f(g(x)) = h(x) = (3x + x^2)^0.5; 2. Express the distance between the point (3, 0) and point P(x, y) of the parabola y = x^2 as a function of x 3. Determine whether converges or diverges. If it converges, evaluate the integral
Differentiate the function f(x) = ln(2x + 3). Find . lim e^ 2 x/(x+5)^3 →∞ Apply l'Hopital's rule as many times as necessary, verifying your results after each application. Evaluate ∫ x sinh(x)dx . Determine whether 2 ∫ (x / ^(4-x^2)) (dx)
Use implicit differentiation to find an equation of the line tangent to the curve x3 + 2xy + y3 = 13 at the point (1, 2). What is the maximum possible area of a rectangle inscribed in the ellipse x2 + 4y2 = 4 with the sides of the rectangle parallel to the coordinate axes? 3 . Evaluate ∫ dt / (t+1)^
Evaluate ∫3x+3 / x^3-1 (dx) Use trigonometric substitution to evaluate ∫1 / ^/¯1+x2(dx) Determine whether converges or diverges. If it converges, evaluate the integral. ∞∫-∞ 1 / 1+x2 (dx)
Evaluate ∫(^/¯x+4)^3 / 3^/¯x(dx) ∫x2sin2x dx ∫ sin5xdx
Evaluate: ∫ sinh6 xcosh xd x Given ?(x)= csch^-1 1 /x2 find ?'(x) Given ?(x)=log10x find ?'(x).
Find an upper and lower bound for the integral using the comparison properties of integrals. 1∫0 1 /x+2(dx) Apply the Fundamental Theorem of Calculus to find the derivative of: h(x)= x∫2 ^/¯u-1dx Evaluate: 4∫1 (4+^/¯x)^2 / 2^/¯x (dx) Evaluate: ∫2cos^2 xdx Sketch
1. Use the composite Trapezoidal Rule with indicated values of n=4 to approximate the following integrals See Attached file for integrals. 2. Use the Excel programs for Simpson's composite rule to evaluate integrals in Problem 1. 3. Use Gaussian Quadratures with n = 2, n = 4, n = 5 to evaluate integrals in Problem 1.
• Find an estimate of the area under the graph of between and above the -axis. Use four left endpoint rectangles. • Find an estimate of the area under the graph of between and above the -axis. Use four right endpoint rectangles. • Find an estimate of the area under the graph of between and . Use four left
Let RI be the set of functions that are Riemann Integrable. Disprove with a counterexample or prove the following true. (a) f in RI implies |f| in RI (b) |f| in RI implies f in RI (c) f in RI and 0 < c <= |f(x)| forall x implies 1/f in RI (d) f in RI implies f^2 in RI (e) f^2 in RI implies f in RI (f) f^
Please see attached file for full problem description. 1. What is the average value of the function f in Figure 6.4 over the interval ? From the graph, we can approximate: The average value of f on the interval from 1 to 6 is 3. Find the average value of over the interval [0, 2]. The average value
Please see attached file for full problem description. 16. An old rowboat has sprung a leak. Water is flowing into the boat at a rate given in the following table. t minutes 0 5 10 15 r(t), liters/min 12 20 24 16 (a) Compute upper and lower estimates for the volume of water that has flowed into the boat during the 1
Please see attached file for full problem description. Section 5.1 p. 224: 7 7. Figure 5.4 shows the velocity, v, of an object (in meters/sec). Estimate the total distance the object traveled between t = 0 and t = 6. We can estimate this using 1 second intervals. Since the velocity is increasing on the interval
Please see attached file for full problem description. 7. Figure 5.4 shows the velocity, v, of an object (in meters/sec). Estimate the total distance the object traveled between t = 0 and t = 6. We can estimate this using 1 second intervals. Since the velocity is increasing on the interval from t = 0 to t = 6, the lo
Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by a is congruent to b (mod m) - if a - b is exactly divisible by m, i.e., if a - b is an integral multiple of m. Show that this is an equivalence relation , describe the equivalence set, and state the number of distinct equivalence sets.
Topology Sets and Functions (XLVII) Functions Let I be the set of all integers and let m be a fixed positive integer. Two integers a and b are said to be congruent modulo m-symbolized by
What is the integral of x ln x dx? ∫xlnx dx
What is the area between f(x) = x^3 - 4x and the x-axis for the interval x = -2 to x = 2?
Please see the attached file for the fully formatted problems. Suppose that X and Y are continuous random variables with the joint probability density function k(x+y) for 0<x<1,0<y<2 f(x,y) = 0 otherwise (a) Find k, E(X), E(Y), V(X), V(Y), and Cov(X, Y). (b) Are X and Y independent ? (c)
1. Evaluate 2) 2. Differentiate the function f(x) = ln(2x+3) 3. Find lim x∞ (e2x / (x + 5)3). Apply L'Hopital's rule as many time as necessary, verify your results after each application. 4. Evaluate ∫xsinh(x)dx See attached file for full problem description.
1.R is the region that lies between the curve y = (1 /( x2 + 4x + 5) ) and the x-axis from x = -3 to x = -1. Find: (a) the area of R, (b) the volume of the solid generated by revolving R around the y-axis. (c) the volume of the solid generated by revolving R round the x-axis. 2.Evaluate: ∫ sinh6 x cosh xdx.
Please help with the following problem. Provide step by step calculations for each. The average value of f(x) = 1/x on the interval [4, 16] is (ln 2)/3 (ln 2)/6 (ln 2)/12 3/2 0 1 none of these Find the area, in square units, of the region b
Stokes Theorem. See attached file for full problem description. Use Stokes Theorem to evaluate....
4. A quantity of gas with an initial volume of 1 cubic foot and a pressure of 2500 pounds per square foot expands to a volume of 3 cubic feet. Find the work done by the gas for the given volume. Assume that the pressure is inversely proportional to the volume. 6. Find moment of mass M_x, M_y, and center of the mass for the la
#7,8 and 9 Please see attached file.
10. Stock Values. Integrated Potato Chips paid a $1 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 4 percent per year. 1. What is the expected dividend in each of the next 3 years? 2. If the discount rate for the stock is 12 percent, at what price will the stock sell? 3. What is the exp