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Sketch the circles in Exercises 53–56. Give polar coordinates for their centers and identify their radii. 53. r = 4 cos u 54. r = -2 cos u 55. r = 6 sin u 56. r = -8 sin u

The digestion time in hours of a fixed amount of food is exponentially distributed with a mean of 1 ...

A brief calculation shows that if 0&lt;=x&lt;= 1, then the second de-rivative of ƒ(x) = sqrt(1 + x4)...

Why is the exponential model unrealistic for predicting long-term population growth? How does the lo...

Evaluate the limit, if it esxists. (If an answer
does not exist, enter DNE.).
lim x°-4I+3
x>3
X-3

Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the exa...

Consider the infinite region in the first quadrant bounded by the graphs of y = 1 /x2 , y = 0, and x...

Plot the following points (given in polar coordinates). Then find all the polar coordinates of each ...

The parabola x2 = -4y is shifted left 1 unit and up 3 units to generate the parabola (x + 1)2 = -4(y...

What values of p have the following property: The area of the region between the curve y = x^-p, 1&l...

Find the area under one arch of the cycloid x = a(t - sin t), y = a(1 - cos t).

For the function f,Construct and simplify the difference quotient f(x+h)-f(x)/h

What is the binomial series? On what interval does it converge? How is it used?

I need to compute each limit. The limit is ...
lim x -&gt; -3
x2 + x - 6
—————
x3 + 27

The “triangular” region in the first quadrant bounded by the x-axis, the line x = 4, and the hyperbo...

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)= 6/((x^2)-16) 
Where is the function concave up and down in interval notation...

Use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your c...

Solve the inequality. Write your answer in interval notation.
-7x &gt; -2x2 + 15

Graph y = log a 2 as a function of a over the interval 0&lt;a&lt;= 4.

Consider the following two equations.
уд
Find the values of x for which f(x) = g(x).
a.

How do you reindex a series? Why might you want to do this?

In Exercises 13–18, solve for y.
13. 3^y = 2^(y+1)
14. 9e^2y = x^2
15. ln ( y - 1) = x + ln y
16. 4^...

Solve the initial value problem
dy/dt+ xy = x, y(0) = -6

a. Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u.
b. Fi...

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

Find the point on the parabola x = t, y = t2, -infinity&lt;=t &lt;=infinity, closest to the point (2...

Use the identity sin^2 x = (1 - cos 2x)/2 to obtain the Maclaurin series for sin^2 x. Then different...

Find the length of the curve y = ln(e^x - 1) - ln(e^x + 1), ln 2&lt;=x&lt;= ln 3.

Find all polar coordinates of the origin.

Besides geometric series, what other convergent and divergent series do you know?

Could x^(ln 2) possibly be the same as 2^(ln x) for some x&gt; 0? Graph the two functions and explai...

Express in terms of sums and differences of logarithms

This question has several parts that must be completed sequentially. If you skip a part of the quest...

A girl is sliding down a slide shaped like the curve y = 9e^(-x/3). Her y-coordinate is changing at ...

In the function: 
f(x)= (3x^2)ln(x) , x&gt;0
What are the x-coordinates of all local minima and mini...

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

The region in the first quadrant enclosed by the coordinate axes, the curve y = ex, and the line x =...

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

In the function: 
f(x)= (3x^2)ln(x) , x&gt;0
What are the vertical asymptotes?

A 200-gal tank is half full of distilled water. At time t = 0, a solution containing 0.5 lb /gal of ...

What is an infinite series? What does it mean for such a series to converge? To diverge? Give exampl...

lim x → 0− g(x)

 

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

A ball with mass 0.15 kg is thrown upward with initial velocity 20 m/s from the roof of a building 3...

What do you know about rearranging the terms of an absolutely convergent series? Of a conditionally ...

) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)?
Consider the function f(x) whose second ...

Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant bo...

Write equations for the asymptotes for the graph of
2 + Sr - 3
f(x) =

Sketch the circles in Exercises 53–56. Give polar coordinates for their centers and identify their radii.53. r = 4 cos u54. r = -2 cos u55. r = 6 sin u56. r = -8 sin u

Note: We&rsquo;ll answer the 53rd question since we answer only one question at a time. Please submit a new question specifying the one you&rsquo;d like answered.Sketch the circles Give polar coordinates for their centers and identify their radii.&nbsp;r = 4 cos u

Calculus

Math

Sketch the circles in Exercises 53–56. Give polar coordinates for their centers and identify their radii.
53. r = 4 cos u
54. r = -2 cos u
55. r = 6 sin u
56. r = -8 sin u

Sketch the circles in Exercises 53–56. Give polar coordinates for their centers and identify their radii. 53. r = 4 cos u 54. r = -2 cos u 55. r = 6 sin u 56. r = -8 sin u

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