Chapter . 5

Problem Statement

{1,2,3,4,6,9,12,18,36}
$n+3
{3}
12+36/$n
$c+$a
$c+2*$a
$c+3*$a
$a*$c
round(pow(cos(3.1416/$a),2),4)
round(pow(cos($n1*3.1416/$d),2),4)
round(pow(cos($n2*3.1416/$d),2),4)
round(pow(cos($n3*3.1416/$d),2),4)
round((3.1416/$c)*($ans1+$ans2+$ans3+$ans4),4)

Calculate the L4 approximation for on .

Step 1

To calculate rectangular approximations to area using the left-endpoint with four subintervals, L4, for the given function, divide into equal subintervals so that the width of each rectangle is , where a, b are the endpoints of the interval and N is the number of rectangles.

Question Sequence

Question

jPh4A9ffX/NMWp7yYCBQ3kHkm+Yiq0o7tR5l7KzvN9n1s2SRSt+OespOL3bEpEn+h0mAXEY6I5k8zsIun4DnXGtGP16bgnu3TXIIRS5A5wSeqQb4xIZJnwWfM/QhiyYYqiQsWVTLJ16dMhksN73kYaKo+O7SsRCCOouxJR8ujlTUCtaiRYiOIG0fKu+Aq6X8Sk5OC5Y5MlsBt/5AkwK/rSqzFPqHEE9uvX3YDlFnf2EiJAoZfE2Einy3W5W/eHkJZIJ+vdgcQ51ACx8cxjzbNqzcAQCZx05FNNUqWAfsREHpQAbuprAxe+Wl6Cp37zflSCr0SrwSA5qh5tLMimjjhRzWRjJ121J/LnWly3GE7B5lKsaSsuabFkM80MO3NidM9LdtVHvyIKzjM0sSF/jEnABTCZgbO14jawjsZYo2SW4yPZhTZQ7IROPv0Saav+1EvxYsrWMmjR15PJnuB/ZBJuoNtUckgg91PxgggGUm41Jw6AGg2HkSNzL12kS7nQ8BobohDGjtoZm+YOLrb//LFt3djH+dG1ET+W+00wgqB0efeNqtqZgh4QtNXdUaQj7AEXdmbQdSAWwYd1yBYxhxa10nz1ouvwIWhTzEbF3OHObNWICi05AhReCANxDVhEAz7ilFj4W3iMo6F+cxLLehm/wIVUKqNsMpSM/DiLJI+vesCUAHdHf6cL3VoFTL5mghkl1jz/YpkOxMxkUoRB34A5qxN0XVKNdNmuXD9Xjd7QpbnM1ju8aPFKFm2wqe68g21dC/MXX2+R6R+tmTUjp9qObEff8xFcbQd4L5o7P9PfbXbWpAVmVhqisWViZllZFfi29Oa9sEVAKBtUugcQCdwc7Ivq4BICQLqM8QxD2Ugxjiw8L4U2GV9LI9Vfvy+F3ZGox3WzraCQZMk22PKoij8XAxwkReJs6TOnWPqCbqBtweEy6tJe5nT/Zve7rjPIh/XF/1n18Jv3U4clNQ5dB6c62ByC8CyoaIZj+1/sv0S79NRtn1trekV2kgwsBbfXuzr/Qvgc6m9LOHXjDmJu0vKbyLDgMyaiguloJCS7g0qBnJ/KmCSeIEFaAwH0wfCo/YYjAO92WGR2EoOtq9OXdq8mhDFrxhChdpnNzoyE98HCtPPNlcvkYxSBSjAV5MWwsCzKuDQaD7KzCqzlKPHINEt6lhWK9EYmmbBKv03i0rdyMK3tuf3e8NUzlULZO0Bvc0Ejejkg7iyDWhH4Eohll6N8yYPpb797hiGA+q3zlEZZOPcgbPQhsndQikO1hb0gvc5kf+y5xzHHT1lipMrKizuqGryNpFz0h6AgYp+3iQV5DTtCVgq+YoM5MuGP/yg2bBYrxI+ne1+2WdGQ9M+uO/ZBKgOyXd7T2OHVjjyZ5PL02wVy+wnXZVnIp+WzVK29L9nV6qBnrn9Ix5dEz3q9VnjarmMMZFWmKSV4OO4YVjwodDoyXc+qcvyzN87lkWrjFZAM7dJ/1iAgvjY+LwToBWkQDBIfJdW50+Z2orradx+/cyo8q7h3Dl4cep++Xc9LRgKB1YwzHOkDVNzyiulUFuEXJfnIoSt6nzjU0zHB1QkG6rldVZ5aeadhLK+ik0x7kbu+nUintogVNO4nJwWuMO7ZAijPauh8AStirAEnrd3q12fKDJriz1NFZ7yS7PhxNPtSec6t2Sq2mQ11UTLRwbX5CNACiIzAmguE+EN35ZVfkySAr+P502QobGILlQQjq1VD05/FklO6oEZ069QsVcttUKKMn74AS1UEuzG/r3KIA=
Correct.
Incorrect.

Question

Since we are using left endpoints, the first left endpoint x-value, x1, is 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

Correct.
Incorrect.

Step 2

The formula for left-endpoint approximation is .

Substitute N = 4 and in the formula and simplify.

Question Sequence

Question

For find .

(Round your answers to four decimal places.)

UFPfACDOxzX9rlDg

2Og4UEB2nw1H7dPo

fpzogoeOkbmsBux4

6Yvgt1+y5CRhi2UG

Correct.
Incorrect.

Step 3

Question

Using the values found in step 2, find the approximation of over the given interval correct to four decimal places.

rSnPCAHRLeo=

Correct.
Incorrect.