3. 9-12 Use the Midpoint Rule with the given value of n toapproximate the integral. Round the answer to four decimalplaces.9. fsin√xdx, n = 411.2XJo x + 117. limn→∞17-20 Express the limit as a definite integral on the giveninterval.n sin Xi1 + Xin20. limn→∞ndx, n = 518. lim Σx;√√1 + x²³ Ax, [2,5]n→∞ i=1i=1nΔ.x, [0, π]19. lim [5(x)³ - 4x*] Ax, [2,7]n→∞i=1110. f¹ √√x³ + 1 dx, n = 512. fx sin²x dx,x*(x*)² + 4n = = 4Ax, [1,3]

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Answered: 9-12 Use the Midpoint Rule with the…

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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1) Calculate the area (A) of the limit domain by the equation curve y=1/x, x=(n-1), x=(x+1) and the axis. n>1 2) By using the Simpson method, show that A= 1/3*((1/(n-1))+(4/n)+(1/(n+1))) We will divide the interval [(n-1),(n+1)] into 2 sub-intervals of equal length. 3) Show that ¦E¦ = 4/15n5 where E is the error made in order 5.
1. a) Find the area of the region lying between f(x) = x^2 − 3x + 2 and x − axis between x= 2and x = 4 by the limit definition. 1. b) Check your answer in a) by finding a definite integral.
Suppose that r1 and r2 are roots of ar2 + br + c = 0 and that r1 ≠ r2; then exp(r1t) and exp(r2t) are solutions of the differential equation ay″ + by′ + cy = 0. Show that ϕ(t; r1, r2) = (exp(r2t) − exp(r1t))/(r2 − r1) is also a solution of the equation for r2 ≠ r1. Then think of r1 as fixed, and use l’Hôpital’s rule to evaluate the limit of ϕ(t; r1, r2) as r2 → r1, thereby obtaining the second solution in the case of equal roots.
7.7 11) Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to approximate the given integral with the specified value of n.
12. Evaluate the triple integral xyz dxdydz for the following limits: z from 0 to y, y from 0 to 4, and x from 0 to1. 17.Find the limit of sin2x/sin3x as x approaches to 0.
Using the definition of integral12. x^2 dx as a limit of a sum of rectangles, compute integral12. x^2 dx. (Hint: You will likely need to use the facts that Sigmai=1n i^2= n(n+1)(2n+1)/6 and Sigmai=1n i= n(n+1)/2)
7.7 5) Use the Midpoint Rule to approximate the given integral with the specified value of n. Compare your results to the actual value to determine the error in each approximation.
Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY
I now know about the even function rule where you can change the bounds from -a to a to 0 to a by putting a 2 out front of the integral for any "even function." After asking my first question about that the new solution did not use that method and instead used -2 to 2 as in the original problem, this makes the answer 0 and if you use the even function method and pull the 2 out front the answer is pi/2. Which of these is the correct answer? How do we know when we can use that even function rule or when not to. I noticed the rule said an even function is when f(-x)=f(x) but I'm not exactly sure what that means
If g(x)= ((x^2)-4)/(-x-3) and h(x)= g(x), evaluate (integral^-4 with an index of -5) h(x) dx Answer options are 1. -9 2. 6 3. 45/2 4. 3/2 5. 2
Use Simpson's 3/8 rule to compute the approximated solution where f (x) = 1/Cosx + 4 defined at the interval (1,4.5) and n = 7
Consider the following initial value problem. a) Find the solution y(t) in an explicit form. b) Use the theory of limits to find the behavior of y(t) as t approaches -infinity and +infinity.

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