Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
| π/2 |
| 0 |
| 3 | 1 + cos(x) |
dx, n = 4
In: Math
1) Find the Taylor series (to second order terms) of the function f(x,y) = x^2 −4x + y + 9 around the point x = 3, y = −1.
2)Explain why the corresponding Taylor Series (to third order
terms) will be the same as the second-order series.
In: Math
y''(t)+(x+y)^2*y(t)=sin(x*t+y*t)-sin(x*t-y*t), y(0)=0, y'(0)=0, x and y are real numbers
In: Math
Find the first 3 nonzero terms of the Maclaurin series for the function and the values for which the series converges absolutely.
f(x)= x^4 * e^x^2
In: Math
give a) Domain b) VA c) HA* d) OA* e) y-int f) x-int for each
2) f(x) = 4 /3x - 9
3) g(x) = (x -1)(x + 4) /(x + 1)(x - 5)
4) h(x) = x ^2 + 4x/ x + 6
5) j(x) = x ^2 - 4 /(x + 2)(x - 3)
In: Math
A typical thickness for a sheet of paper is 0.004 inches. If you
fold a sheet of paper once, the thickness of
the folded paper will double to a value of 0.008 inches. A second
fold will result in a folded thickness of
0.016 inches. Create a spreadsheet that shows the number of folds
from 0 to 50 and the resulting
thickness of each fold. Calculate the resulting thickness in units
of inches, feet, and miles.
In: Math
The base of a solid is the segment of the parabola y2 = 12x cut off by the latus rectum. A section of the solid perpendicular to the axis of the parabola is a square. Find its volume.
In: Math
The value of the cumulative standardized normal distribution at Z is 0.8925. Calculate the value of Z.
In: Math
Vectors in the plan.
Define scalar product and explain the relationship between scalar product defined by coordinates respectively at lengths and angles between vectors.
Significance of the scalar product sign.
The determinant of a vector pair.
In: Math
Consider the curve given by the equation y^2 - 2x^2y = 3
a) Find dy/dx.
b) Write an equation for the line tangent to the curve at the point (1, -1).
c) Find the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal. d) Evaluate d 2y /dx2 at the point (1, -1).
In: Math
complete the following activities with these cricket chirp data.
Temperature (F degree) 69.7, 93.3, 84.3, 76.3, 88.6, 82.6, 71.6, 79.6
Chirp in 1 minute 882, 1188, 1104, 864, 1200, 1032, 960, 900
1. Find the regression models (linear and quadratic) for the above data
a. What is the equation for the line of best fit in y=mx+b form?
b. What is the equation for the best fitting quadratic model?
2. Use your models (not the actual data) and calculators to predict the number of chirps at each of the three temperatures.
| Linear | Quadratic | |
| 69.7 | ||
| 76.3 | ||
| 88.6 |
In: Math
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Passing through ( −3,−4) and (2,6)
What is the equation of the line in point-slope form?
__
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
What is the equation of the line in slope-intercept form?
__
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
In: Math
A conical container of radius 10ft and height 40ft is filled to a height of 38 ft of a liquid weighing 62.4 lb/ft^3. How much work will it take to pump the contents to the rim? How much work will it take to pump the liquid to a level of 2 ft. above the cone's rim?
In: Math
| Let f (t) =
|
| (a) | f (t) can be written in the form g1(t) + g2(t)U(t − 2π) + g3(t)U(t − 4π) where U(t) is the Heaviside function. Enter the functions g1(t), g2(t), and g3(t), into the answer box below (in that order), separated with commas. |
| (b) | Compute the Laplace transform of
f (t). |
In: Math
In: Math