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If cos x is replaced by 1 - (x2/2) and |x |<0.5, what estimate can be made of the error? Does 1 - (x2/2) tend to be too large, or too small? Give reasons for your answer.

find the center of mass of a thin plate of constant density d covering the given region.
1. The regi...

a ball is thrown straight upwards from a tower (40 feet high) so that its position, s in feet, at ti...

How would you compare the relative merits of Simpson’s Rule and the Trapezoidal Rule.

In the theory of relativity, the Lorentz contraction formula

L = L0



 
1 − v2/c2





expresses t...

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Find the volume generated by revolving one arch of the curve y = sin x about the x-axis.

In the function: 
f(x)= (3x^2)ln(x) , x&gt;0
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The temperature of an ingot of silver is 60°C above room temperature right now. Twenty minutes ago, ...

(sin t)y′+(cos t)y=et,y(1)=a,0&lt;t&lt;π

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Find the volume using the shell method.
x = 8y2, y ≥ 0, x = 8;  about y = 2

What are the integrals of tan x and cot x? sec x and csc x?

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

Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the li...

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

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

You are looking for an item in an ordered list 450,000 items long (the length of Webster’s Third New...

Find the area of the surface generated by revolving the curve y = sqrt(x2 + 2), 0 &lt;=x&lt;=sqrt(2)...

What integrals lead to logarithms? Give examples.

Find an equation of the line that passes through the given points. (Let x be the independent variabl...

Find the volume of the solid that results when the shaded region is revolved around the indicated ax...

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

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The region enclosed by the curve y = sech x, the x-axis, and the lines x = +- ln sqrt(3) is revolved...

Use the given transformation to evaluate the integral.
lr a?dA, where R is the region bounded by the...

Find the centroid of a thin, flat plate covering the “triangular” region in the first quadrant bound...

consider the equation f(x) =5x2
find the average rate of change between x=3 and x=3+x

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^...

Find the length of the curve y = x2, 0 &lt;=x &lt;=sqrt(3)/2.

I need help evaluating a derivative of a function at the point (pi/2,18pi)

Use the theorems of Pappus to find the lateral surface area and the volume of a right-circular cone.

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Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200...

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

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

Find the centroid of the region bounded by the graphs of y = x + cos x and y = 0 for 0&lt;=x&lt;= 2p...

solve the following equation for X.
3*e^2x+7*e^x+2=0

In the function: 
f(x)= (5x)/((x^2)-25 
How do you find the x-values of the inflection points? 
Wher...

Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.
x...

In Exercises 1–3,
a. Identify the equilibrium values. Which are stable and which are unstable?
b. Co...

Suppose that q = f(p) is the demand curve for a product, where p is the selling price in dollars and...

We&rsquo;ll answer the second question first. Notice the question have used first two digits of Maclaurin series for cosx. This is an alternating series, irrespective of whether x is positive or negative.

For small x the factorials in the denominator will dominate the powers of x in the numerator, so the terms will definitely decrease in magnitude. So it will tend to 0, since the cosine series converges for every x. Thus the conditions for the Alternating Series Test and Alternatin...

Calculus

Math

If cos x is replaced by 1 - (x2/2) and |x |&lt;0.5, what estimate can be made of the error? Does 1 - (x2/2) tend to be too large, or too small? Give reasons for your answer.

If cos x is replaced by 1 - (x2/2) and |x |<0.5, what estimate can be made of the error? Does 1 - (x2/2) tend to be too large, or too small? Give reasons for your answer.

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