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Write inequalities to describe the sets in Exercises 45–46. 45. The half-space consisting of the points on and below the xy-plane 46. The upper hemisphere of the sphere of radius 1 centered at the origin

What is Taylor’s formula? What does it say about the errors in-volved in using Taylor polynomials to...

4. Recall that the set of Complex Numbers is defined as C = {z| z = a + ib, where a,b eR and i = v-1...

Show that the number 4p is the width of the parabola x2 = 4py (p&gt;0) at the focus by showing that ...

Find the average rate of change of the given function between the following pairs of x-values.  f(x)...

In the function: 
f(x)= (7x+B)/(4x+b) , with 7b&gt;4B
When is the function increasing and when is th...

The parabola y2 = 8x is shifted down 2 units and right 1 unit to generate the parabola ( y + 2)2 = 8...

What are the standard equations for lines and conic sections in polar coordinates? Give examples.

What is an improper integral of Type I? Type II? How are the values of various types of improper int...

Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

 lim h→0




(5 + h)−1 ...

Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
A(1, ...

(3x2 − 2xy + 2) + (6y2 − x2 + 3)y′ = 0

describe the given set with a single equation or with a pair of equations.The line through the point...

Consider the function.
|r + 7|– |r – 7|
f(x) =
Estimate the following by evaluating fat x-values nea...

Show that
a. cosh iu = cos u,
b. sinh iu = i sin u.

Connect the two points (1, d(1)) and (3, d(3)) with a straight line.

Replace the Cartesian equations in Exercises 56–61 with equivalent polar equations.
56. x - y = 3
57...

a. Graph the hyperbolic spiral ru = 1. What appears to happen to c as the spiral winds in around the...

The line segment joining the points (0, 1) and (2, 2) is revolved about the x-axis to generate a fru...

Suppose that a sum S0 is invested at an annual rate of return r compounded continuously.
a.Find the ...

Solve the initial value problem
 
and determine the interval in which the solution is valid.Hint: To...

Find the first four terms of the binomial series for the functions in Exercises 1–4.
1. (1 + x)^1/2
...

Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

The autonomous differential equations in Exercises 9–12 represent models for population growth. For ...

In the function: 
f(x)= (7x+B)/(4x+b) , with 7b&gt;4B
What are the critical numbers of the function?

solve for x by completing the square
x2 + 14x -3 =0

Given cost and price functions C(q)=120q+45,900 and p(q)=-2.3q+840, what price must the company set ...

I need to compute each limit. The limit is ...
lim x -&gt; 1
x - 1 
—————
2 - the square root of x +...

In the function: 
f(x)= (3x^2)ln(x) , x&gt;0
Where is the function increasing and decreasing in inte...

What is the expected value of a continuous random variable? What is the expected value of an exponen...

Use a calculator to estimate the limit.
6x
lim
8x

use I=60/13(1-e-13t/5) to express the time t as a function of the current I

Find the volume swept out by revolving the region bounded by the x-axis and the graph of
x = 2t, y =...

if you have a parametric equation grapher, graph the equations over the given intervals x = 2 cos t ...

Exercises 45–48 give equations for parabolas and tell how many units up or down and to the right or ...

Find the center C and the radius a for the sphere
1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9
2. x2 + y2 + z2 -...

Find the distance from the point (-2, 1, 4) to the
a. plane x = 3
b. plane y =-5
c. plane z =-1

Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test. L...

What substitutions are made to evaluate integrals of sin mx sin nx, sin mx cos nx, and cos mx cos nx...

What is a reduction formula? How are reduction formulas used? Give an example.

Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x2 + 4y2 = 3...

lim x → 0− g(x)

 

lim x → 0+ g(x)
Is g continuous at x = 0?

Exercises 17–20 give equations for ellipses. Put each equation in stan-dard form. Then sketch the el...

Find polar equations for the circles in Exercises 57–58. Sketch each circle in the coordinate plane ...

a ball is thrown straight upwards from a tower ( 40 feet high) so thats its position, s in feet, t i...

What theorem sometimes enables us to use l’Hôpital’s Rule to calculate the limit of a sequence? Give...

Solve the homogeneous equations
x2 dy + ( y2 - xy) dx =0

Write inequalities to describe the sets in Exercises 45–46.45. The half-space consisting of the points on and below the xy-plane46. The upper hemisphere of the sphere of radius 1 centered at the origin

Since we only answer up to 1 question, we&rsquo;ll answer the first question. Please resubmit the question and specify the other question number you&rsquo;d like answered.To determine the equation of the half space consisting of the points on and below xy-plane.

Given:The points lie on and below the xy-plane.

The equation space with points on the xy-plane is z=0.The equation space with points below the xy-plane i...

Calculus

Math

Write inequalities to describe the sets in Exercises 45–46.
45. The half-space consisting of the points on and below the xy-plane
46. The upper hemisphere of the sphere of radius 1 centered at the origin

Write inequalities to describe the sets in Exercises 45–46. 45. The half-space consisting of the points on and below the xy-plane 46. The upper hemisphere of the sphere of radius 1 centered at the origin

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