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Suppose that f(x) is a continuous function on (2,7), positive on (2,5) and negative on (5,7)...
Problem 4. (6 pts) (a) Suppose that f(x) is a continuous function on 2,7], positive on...
Problem 4. (6 pts) (a) Suppose that f(x) is a continuous function on 2,7], positive on (2,5) and negative on (5, 7). « [ r(a) dr = 11 and ſsaw) dr = 3, then ind ſis(2) dr. .10 f(x) (b) Suppose that is an even and integrable function. If "L" 3, . f(x) da = 5, then find L" (a) dr.
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to f...
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to find .后f(x)dr Problem 2. Consider the function -2, zEQ 2, O f(r) = Show that f is not Riemann integrable on 0,1 but s Reemann integrable on this interval. Problem 3. (a) Let f be a real-valued function on a, b] such thatf()0 for all c, where c E [a, b Prove that f is Riemann integrable on a, b...
Suppose that f(x) is a non-negative and continuous function on the interval (a, b). The following...
Suppose that f(x) is a non-negative and continuous function on the interval (a, b). The following method (illustrated in the below figure) is a well-known method to approximate the total area underneath the curve of f(x) on the given interval: b - a • Divide the interval [a, b] into 5 subintervals each of width 5 • For each 1 Si< 5, choose any arbitrary point c; in the ith subinterval. • Thus, the total area underneath the curve of...
nts) Suppose that f(x) is continuous. The table below shows where f'(a) and f"() are positive and negative....
nts) Suppose that f(x) is continuous. The table below shows where f'(a) and f"() are positive and negative. Draw a graph that matches the information.
nts) Suppose that f(x) is continuous. The table below shows where f'(a) and f"() are positive and negative. Draw a graph that matches the information.
Let f be a positive, continuous, and decreasing function for x 2 1, such that a,...
Let f be a positive, continuous, and decreasing function for x 2 1, such that a, = f(n). Note that if the series, converges to S, then the remainder R - S - Sis bounded by OSRNS / (x) dx. Use these results to find the smallest N such that RN 30.001 for the convergent series.
Suppose that f() is a non-negative and continuous function on the interval [a,b]. The following method...
Suppose that f() is a non-negative and continuous function on the interval [a,b]. The following method (illustrated in the below figure) is a well-known method to approximate the total area underneath the curve of f(x) on the given interval: • Divide the interval [a, b] into 3 subintervals cach of width • For each 1 <is 3, choose any arbitrary point in the ith subinterval. • Thus, the total area underneath the curve of f(x) can be approximated by: 3...
Problem 5 (7 point) Suppose that f'(x) is continuous and that F(x) is an antiderivative of...
Problem 5 (7 point) Suppose that f'(x) is continuous and that F(x) is an antiderivative of f(x). You are given the following table of values: r=0 2 = 2 * = 4 x = 6 -2 6 f(x) 6 F(x) 7 2 -4 -3 2 -4 5 3 (a) Evaluate | ((z) – 3)s -3)?f'(x)dx. (b) Evaluate (* 25 r* f" ()dx
6.59. Let f be a continuous function on [a, b]. Suppose that there exists a positive...
6.59. Let f be a continuous function on [a, b]. Suppose that there exists a positive constant K such that If(x) <K for all x in [a, b]. Prove that f(x) = 0 for all x in [a, b]. *ſ isoidi,
3. Suppose lim s(a) dr = co, where f(a) is a positive, decreasing and continuous function....
3. Suppose lim s(a) dr = co, where f(a) is a positive, decreasing and continuous function. Which of the following statements is true about the series f(n)? Choose one. n=1 *Please write the letter of your choice. (a) The series converges too. (b) The series converges, but not necessarily to o. (c) The series diverges. (d) The given information is not enough to determine if the series converges or diverges.
Let {h} be a sequence ofRiemann integrable functions on [a,b], such that for each x, {h(x)) is a decreasing sequence. Suppose n) converges pointwise to a Riemann integrable function f Prove that f(x)...
Let {h} be a sequence ofRiemann integrable functions on [a,b], such that for each x, {h(x)) is a decreasing sequence. Suppose n) converges pointwise to a Riemann integrable function f Prove that f(x)dxf(x)dx. lim n00
Let {h} be a sequence ofRiemann integrable functions on [a,b], such that for each x, {h(x)) is a decreasing sequence. Suppose n) converges pointwise to a Riemann integrable function f Prove that f(x)dxf(x)dx. lim n00
Problem 4. (6 pts) (a) Suppose that f(x) is a continuous function on 2,7], positive on (2,5) and negative on (5, 7). « [ r(a) dr = 11 and ſsaw) dr = 3, then ind ſis(2) dr. .10 f(x) (b) Suppose that is an even and integrable function. If "L" 3, . f(x) da = 5, then find L" (a) dr.
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to find .后f(x)dr Problem 2. Consider the function -2, zEQ 2, O f(r) = Show that f is not Riemann integrable on 0,1 but s Reemann integrable on this interval. Problem 3. (a) Let f be a real-valued function on a, b] such thatf()0 for all c, where c E [a, b Prove that f is Riemann integrable on a, b...
Suppose that f(x) is a non-negative and continuous function on the interval (a, b). The following method (illustrated in the below figure) is a well-known method to approximate the total area underneath the curve of f(x) on the given interval: b - a • Divide the interval [a, b] into 5 subintervals each of width 5 • For each 1 Si< 5, choose any arbitrary point c; in the ith subinterval. • Thus, the total area underneath the curve of...
nts) Suppose that f(x) is continuous. The table below shows where f'(a) and f"() are positive and negative. Draw a graph that matches the information.
nts) Suppose that f(x) is continuous. The table below shows where f'(a) and f"() are positive and negative. Draw a graph that matches the information.
Let f be a positive, continuous, and decreasing function for x 2 1, such that a, = f(n). Note that if the series, converges to S, then the remainder R - S - Sis bounded by OSRNS / (x) dx. Use these results to find the smallest N such that RN 30.001 for the convergent series.
Suppose that f() is a non-negative and continuous function on the interval [a,b]. The following method (illustrated in the below figure) is a well-known method to approximate the total area underneath the curve of f(x) on the given interval: • Divide the interval [a, b] into 3 subintervals cach of width • For each 1 <is 3, choose any arbitrary point in the ith subinterval. • Thus, the total area underneath the curve of f(x) can be approximated by: 3...
Problem 5 (7 point) Suppose that f'(x) is continuous and that F(x) is an antiderivative of f(x). You are given the following table of values: r=0 2 = 2 * = 4 x = 6 -2 6 f(x) 6 F(x) 7 2 -4 -3 2 -4 5 3 (a) Evaluate | ((z) – 3)s -3)?f'(x)dx. (b) Evaluate (* 25 r* f" ()dx
6.59. Let f be a continuous function on [a, b]. Suppose that there exists a positive constant K such that If(x) <K for all x in [a, b]. Prove that f(x) = 0 for all x in [a, b]. *ſ isoidi,
3. Suppose lim s(a) dr = co, where f(a) is a positive, decreasing and continuous function. Which of the following statements is true about the series f(n)? Choose one. n=1 *Please write the letter of your choice. (a) The series converges too. (b) The series converges, but not necessarily to o. (c) The series diverges. (d) The given information is not enough to determine if the series converges or diverges.
Let {h} be a sequence ofRiemann integrable functions on [a,b], such that for each x, {h(x)) is a decreasing sequence. Suppose n) converges pointwise to a Riemann integrable function f Prove that f(x)dxf(x)dx. lim n00
Let {h} be a sequence ofRiemann integrable functions on [a,b], such that for each x, {h(x)) is a decreasing sequence. Suppose n) converges pointwise to a Riemann integrable function f Prove that f(x)dxf(x)dx. lim n00
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