EXERCISE: 1. Approximate the following integrals using the Trapezoidal rule and Find a bound for the error using the error formula, and compare this to the actual error. dx a- Jas b-

Q: 8.) What is the distance between an airplane flying at 120 feet above sea level and a turtle…

A: We find the distance between an airplane flying at 120 feet above sea level and a turtle swimming at…

Q: Tnd th gredient y te tengut y= 3x at te pont (3,-1)

A: See the detailed solution below.

Q: Find the arclength of y = 3x³/2 on 2 ≤ x ≤ 4

A:

Q: (4g(x) – 1) dx. -3

A: Given: ∫-364g(x)-1 dx To find: The definite integral.

Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: c) Using linear approximation, estimate the value of the function: f ( x) =x cos-1 x at x = 0.1.…

A:

Q: Evaluate the integrat. Sa dx су-хууг dx

A: Given :∫14-x22dx

Q: 2, The hadiusS r of a sphere is increasing as a vate af 3amimin. Find the rate af Ghane e Of Ahe…

A:

Q: Evaluate with the order of integration reversed..... 4 11: x dx dy

A:

Q: Calculate I = Jo 1+x dx where h = 1/6.

A: Please check step 2 for the solution.!

Q: 6. Integrate , v4 – x² dx using trapezoids. Divide[-2,2] into 20 subintervals. Give the answer…

A: Given that, the function is fx=4-x2 and the value of a=-2 and b=2 and n=20. Note that, the formula…

Q: Evaluate: x2dz using trapezoidal method with n = 10. Round off to 6 decimal places.

A: To evaluate using the trapezoidal rule with n=10.

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of f V(1+ x3)dx. Give…

A: Given integral is ∫021+x3dx and h=1. We have to approximate the given integral by using Simpson's…

Q: Use the trapezium rule, with 4 strips, to estimate ? e−x2 dx on [0, 2]. What is the maximum error?…

A:

Q: Find the extremum of f(x,y) = 3x²y² +5y² + 5x?. Answer:

A: Given:- f(x, y) = 3x2y2+5y2+5x2 To find:- Extremum of f(x, y)

Q: 4. Given f(x) = sin² (2x) find the slope at (5, 1) a)-√3 b) √3 d) 0.1395

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Given - sin x dx a) Use Simpson's rule to approximate the value of I using 4 subintervals. b)…

A: As per bartleby guidelines, for more than one questions asked only one has to be solved . Kindly…

Q: Please don't provide handwritten solution ...

A: We need to find "n" so that the error in the approximation of ∫01​x+11​dx is less than 0.00001.…

Q: Approximate -0.2 0.1 cotxdx using N = 8 of the Trapezoidal Rule and calculate the error. Round off…

A:

Q: Evaluate with the order of integration reversed..... -√4-y x dx dy

A:

Q: Find the distance between the following two points: (0, -1) and (2, 0) O 2 O V5 O V13

A:

Q: the length and with of the rectangets are measured at 29 am and 12 cm respectively, with a maximum…

A: It is provided that the length and width of a rectangle are l=29 cm, w=17 cm, respectively. The…

Q: (a) Estimate the area under the curve across the given domain with the "Trapezoidal Rule" using…

A: The integral to be evaluated using Trapezoidal rule is ∫x=-2x=+22x3+3x2-7x+3 dx. The trapezoidal…

Q: Use a tangent plane at the point (4, -—4) to approximate the value of the following function at the…

A: Tangent plane to the surface

Q: Let f(t) = Arcsin(t) and g(x, y) = √/1-x² - y². Find h(x, y) if h = fog. Also, find the domain and…

A: The domain of a function f(x) is the set of all possible values of x for which f is defined. The…

Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: Find the arclength of y = 3x³/2 on 2 ≤ x ≤ 4

A:

Q: Q1: Estimate using composite tiapezoidal rule Sinx the integral sě with h=D0.25

A:

Q: Evaluate 4.x sin(y?) y3 dydx. Hint: reverse the order of integration

A:

Q: Evaluate the integral: ecosx dx using trapezoidal rule (n=5) then find the bounds of error.

A: We have to evaluate the integral  using trapezoidal rule (when n=5).Also, we have to find the bounds…

Q: er Q5:- Find the integral - dx n=8 using Trapezoidal method.

A: