Identifying definite
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- Write the limit as a definite integral on the interval [a, b], where c, is any point in the ith subinterval. Limit lim ||A|| ->0 n i = 1 (5c; + 7) Ax; dx Interval [-9, 9]arrow_forwardExpress the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit. dx Find the width of each subinterval in terms of n. units Find the ith endpoint in terms of n. X; = Evaluate f(x) = V 5 + x² at the ith endpoint. f(x,) = Express the integral as the limit of Riemann sums using right endpoints. lim n- 00 i=1 Need Help? Read Itarrow_forwardExploration and Opinion. We know that definite integral of a continuous function f(x) over interval [a, b] is defined to be the limit of Riemann sum, namely IV 1. [ f(x) f(x) dx = limf(5) Ax 7-1 where a = xarrow_forward(a) Express the area under the curve y =x4 +5x2 +xfrom 2 to 7 as a limit.(b) Use a computer algebra system to evaluate the sum inpart (a).(c) Use a computer algebra system to find the exact areaby evaluating the limit of the expression in part (b).arrow_forward. Let f (x) be a continuous function on [a, b], where a, b ∈ R and a < b. Suppose that there are two sequences(xn) and (yn) satisfying that(a) a < xn < c < yn < b for all n ∈ N, and(b) lim(xn) = c and lim(yn) = c. REFER TO PICTURE AND PROVE IT, WHILE ALSO EXPLAINING EACH STEP IN FULL DETAILarrow_forward(a) Evaluate the definite integral, f (3x² - 4x + 1) dr by calculating it as a limit of a suitable Riemann sum.arrow_forwardarrow_back_iosarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage