Question

Asked Jan 24, 2020

40 views

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.

Step 1

We’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.

Step 2

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...

Find answers to questions asked by student like you

Show more Q&A

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

A: Given information:

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

A: Click to see the answer

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

A: Compare the relative merits of Simpson’s rule and the Trapezoidal rule as given below in the Table

Q: In the theory of relativity, the Lorentz contraction formula L = L0 1 − v2/c2 expresses t...

A: Click to see the answer

Q: Find the volume of the solid generated by revolving the region bounded by the curve x = e^y2 y = 1 a...

A: Click to see the answer

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

A: Let the bounds of one arch of the sine curve be 0 and pi. Then, the volume generated by revolving on...

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

A: Click to see the answer

Q: Find the volume of the solid generated by revolving the region bounded by the curve y = sin x and th...

A: Given:Find the volume of the solid generated by revolving the region bounded by the curve y = sin x ...

Q: The temperature of an ingot of silver is 60°C above room temperature right now. Twenty minutes ago, ...

A: Given,The temperature of an ingot of silver is 60°C above room temperature right now and it was 70°C...