Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is...
Suppose f(x) is continuous and increasing on [a, b] , and concave up on (a, b) .ls TO (the Trapezoid Rule approximation to f(x) dx with n= 6 ) an over-estimate or an under-estimate? Over-Estimate. Under-Estimate. There is not enough information to decide.
Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is S. (the Simpson's Rule approximation to S. f(x) dx with n = 6) an over-estimate or an under- estimate? Over-Estimate. Under-Estimate. There is not enough information to decide.
If f has a continuous second derivative on [a, b], then the error E in approximating by the Trapezoidal Rule is (b- a 12n rmax x)1. asxsb. JE s Moreover, if f has a continuous fourth derivative on [a, bl, then the error E in approximating by fix) dx Simpson's Rule is b-a)s 180a lrmax (x. asxsb. Use these to find the minimum integer n such that the error in the approximation of the definite integral is less than or...
If f has a continuous second derivative on tə, b), then the error E in approximating f(x) dx by the Trapezoidal Rule is IELS (-a) [max 1f"(x)), a sxs b. 12n2 Moreover, if f has a continuous fourth derivative on (a, b), then the error E in approximating Rx) dx by Simpson's Rule is IES (6-a) [max 1(1)(x)), a sxs b. 1804 Use these to find the minimum Integer n such that the error in the approximation of the definite...
10. Suppose the graph of a function is both increasing and concave up on a sx sb. Then, using the same number of subdivisions, and with L, R, and M denoting, respectively, left, right and midpoint Reimann sums, it follows that: (A) RS MSL (B) LSMSR (C) RSM SL (D) LSRSM (E) MSLSR
3. Suppose we estimateſ f(x)dx using our rules with the same number of subdivisions, n but only record three of our estimates: Right(n)=1.8569 Mid(n) = 2.3481 Trap(n) = 2.1627. If f(x)is monotone and does not have any inflection points in the interval [A, B], A. Is f(x) increasing or decreasing? B. Is f(x) concave up or down? C. Estimate the value of Left(n)and Simp(n)
Question 14 Suppose f(x) is an decreasing, concave up function and you use numeric integration to compute the integral of f over the interval [0, 1]. Put the values of the approximations using n = 100 for the left end-point rule (L100), right end-point rule (R100), and Simpson's rule (S100) from the least to the greatest. a) OS100, L100, R100 b) L100, S100, R100 R100, L100, S100 $100, R100, 2100 R100, S100, L100 O None of the above. Review La...
Eunsol Kwon e. Jix) is concave up on [U, OJ Since the grapn is increasing at x = U, the left-most point of this interval Consider the following integral: [x" dx for n € N = {1,2, 3, --}. Now consider the following three statements: is a nonsensical statement. equals the exact area bounded by f(x) = x",x=0, x= 1, and the x-axis. Then Select one: a. All of L., II., and Ill are true. b. II. is the only...
10. Trapezoidal Rule is used to approximate the integral f(a) dx using 1- (yo +2y1 + 2y2 + x-na b-a + 2yn-1 +%),where Use this approximation technique to estimate the area under the curve y = sinx over。 a. π with n 4 partitions. x A 0 B: @ Δy B-A b. The error formula for the trapezoidal rule is RSL (12ba)1 where cischosen on the interval [a, b] to maximize lf" (c)l. Use this to compute the error bound...
9. Determine where f(x) is increasing/decreasing. Locate the local extrema; determine where it is concave up/down, locate inflection pts. Use this information to sketch the graph. (20 pts) 4x2 + 12x – f'(x) = Critical Values are: F"(x) = Possible Inflection points are: First derivative information Interval Sample point f' = + or - Show inc/dec 2nd derivative information Interval Sample point f" x f" = + or - Concavity: