FIGURE 17 13. Let f(x) = x². (a) Sketch the function over the interval [0,2] and the rectangles corre sponding to L4. Calculate the area contained within them. (b) Sketch the function over the interval [0,2] again but with the rect- angles corresponding to R4. Calculate the area contained within them. (e) Make a conclusion about the area under the curve f(x) = x² over the interval [0,2]. 14. Let f(x)=√√x. (a) Sketch the function over the interval [0,4] and the rectangles corre- sponding to L4. Calculate the area contained within them. (b) Sketch the function over the interval [0,4] again but with the rect- angles corresponding to R4. Calculate the area contained within them. (c) Make a conclusion about the area under the curve f(x)=√√x over the interval [0,4]. In Exercises 15-22, calculate the approximation for the given function and interval. 15. L4, f(x)=√√2-x, [0,2] 16. L6, f(x)=√√√6x+2, [1,3] 17. R6. f(x)=2x-x², [0,2] 18. R5, f(x) = x²+x, [-1,1] 19. Ms, f(x) Inx, [1,3] 20. M4, f(x)=2*, [1,3] 21. L4. f(x) = cos² x, [] 22. L6. f(x) = x²+3|x|, [-2,1] In Exercises 23-28, write the sum in summation notation. 23. 47 +57 +6 +77 +87 24. (2+2)+(3+3)+(42 +4)+(5²+5) 25. (22+2)+(23+2)+(24+2)+(25 +2) 26. 1+++++ 2 n 27. + ++ 2.3 (n+1)(n+2) +ex/n 28. e +e+ex/3+.... 29. Calculate the sums: 5 (2) Σ9 30. Calculate the sums: 5 (b) 4 (c) k=2
FIGURE 17 13. Let f(x) = x². (a) Sketch the function over the interval [0,2] and the rectangles corre sponding to L4. Calculate the area contained within them. (b) Sketch the function over the interval [0,2] again but with the rect- angles corresponding to R4. Calculate the area contained within them. (e) Make a conclusion about the area under the curve f(x) = x² over the interval [0,2]. 14. Let f(x)=√√x. (a) Sketch the function over the interval [0,4] and the rectangles corre- sponding to L4. Calculate the area contained within them. (b) Sketch the function over the interval [0,4] again but with the rect- angles corresponding to R4. Calculate the area contained within them. (c) Make a conclusion about the area under the curve f(x)=√√x over the interval [0,4]. In Exercises 15-22, calculate the approximation for the given function and interval. 15. L4, f(x)=√√2-x, [0,2] 16. L6, f(x)=√√√6x+2, [1,3] 17. R6. f(x)=2x-x², [0,2] 18. R5, f(x) = x²+x, [-1,1] 19. Ms, f(x) Inx, [1,3] 20. M4, f(x)=2*, [1,3] 21. L4. f(x) = cos² x, [] 22. L6. f(x) = x²+3|x|, [-2,1] In Exercises 23-28, write the sum in summation notation. 23. 47 +57 +6 +77 +87 24. (2+2)+(3+3)+(42 +4)+(5²+5) 25. (22+2)+(23+2)+(24+2)+(25 +2) 26. 1+++++ 2 n 27. + ++ 2.3 (n+1)(n+2) +ex/n 28. e +e+ex/3+.... 29. Calculate the sums: 5 (2) Σ9 30. Calculate the sums: 5 (b) 4 (c) k=2
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Can you explain question 16 for me in step by step
![FIGURE 17
13. Let f(x) = x².
(a) Sketch the function over the interval [0,2] and the rectangles corre
sponding to L4. Calculate the area contained within them.
(b) Sketch the function over the interval [0,2] again but with the rect-
angles corresponding to R4. Calculate the area contained within them.
(e) Make a conclusion about the area under the curve f(x) = x² over the
interval [0,2].
14. Let f(x)=√√x.
(a) Sketch the function over the interval [0,4] and the rectangles corre-
sponding to L4. Calculate the area contained within them.
(b) Sketch the function over the interval [0,4] again but with the rect-
angles corresponding to R4. Calculate the area contained within them.
(c) Make a conclusion about the area under the curve f(x)=√√x over
the interval [0,4].
In Exercises 15-22, calculate the approximation for the given function and
interval.
15. L4, f(x)=√√2-x, [0,2]
16. L6, f(x)=√√√6x+2, [1,3]
17. R6. f(x)=2x-x², [0,2]
18. R5, f(x) = x²+x, [-1,1]
19. Ms, f(x) Inx, [1,3]
20. M4, f(x)=2*, [1,3]
21. L4. f(x) = cos² x, []
22. L6. f(x) = x²+3|x|, [-2,1]
In Exercises 23-28, write the sum in summation notation.
23. 47 +57 +6 +77 +87
24. (2+2)+(3+3)+(42 +4)+(5²+5)
25. (22+2)+(23+2)+(24+2)+(25 +2)
26. 1+++++
2
n
27.
+
++
2.3
(n+1)(n+2)
+ex/n
28. e +e+ex/3+....
29. Calculate the sums:
5
(2) Σ9
30. Calculate the sums:
5
(b) 4
(c)
k=2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6a0ed01-dc7e-4fee-9bdd-27c695376c3b%2Fac219e92-64bf-4733-bb22-cddadd008db7%2Fy6appdc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:FIGURE 17
13. Let f(x) = x².
(a) Sketch the function over the interval [0,2] and the rectangles corre
sponding to L4. Calculate the area contained within them.
(b) Sketch the function over the interval [0,2] again but with the rect-
angles corresponding to R4. Calculate the area contained within them.
(e) Make a conclusion about the area under the curve f(x) = x² over the
interval [0,2].
14. Let f(x)=√√x.
(a) Sketch the function over the interval [0,4] and the rectangles corre-
sponding to L4. Calculate the area contained within them.
(b) Sketch the function over the interval [0,4] again but with the rect-
angles corresponding to R4. Calculate the area contained within them.
(c) Make a conclusion about the area under the curve f(x)=√√x over
the interval [0,4].
In Exercises 15-22, calculate the approximation for the given function and
interval.
15. L4, f(x)=√√2-x, [0,2]
16. L6, f(x)=√√√6x+2, [1,3]
17. R6. f(x)=2x-x², [0,2]
18. R5, f(x) = x²+x, [-1,1]
19. Ms, f(x) Inx, [1,3]
20. M4, f(x)=2*, [1,3]
21. L4. f(x) = cos² x, []
22. L6. f(x) = x²+3|x|, [-2,1]
In Exercises 23-28, write the sum in summation notation.
23. 47 +57 +6 +77 +87
24. (2+2)+(3+3)+(42 +4)+(5²+5)
25. (22+2)+(23+2)+(24+2)+(25 +2)
26. 1+++++
2
n
27.
+
++
2.3
(n+1)(n+2)
+ex/n
28. e +e+ex/3+....
29. Calculate the sums:
5
(2) Σ9
30. Calculate the sums:
5
(b) 4
(c)
k=2
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