Question

In: Math

a) The following table gives the values of a function f(x) at a certain number of equidistant points on the x-axis.

 

a) The following table gives the values of a function f(x) at a certain number of equidistant points on the x-axis. From the data supplied, calculate approximate values of  by using each of the following rules: (Give the explicit formula/definition for each of the rules, before applying them)

(i) The Trapezoid Rule and (ii) Simpson's Rule.

x =

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

f (x) =

2.7

2.1

2.3

1.7

2.2

2.9

3.1

3.4

3.9

4.9

8.7

b) Use the Midpoint Rule to find the approximation  to 6 decimal places.

Solutions

Expert Solution


Related Solutions

For the following exercises, use the table of values that represent points on the graph of a quadratic function. By determining..
For the following exercises, use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.
The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function...
The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function of time t. Graph f together with the velocity function ?v(t)equals=StartFraction ds Over dt EndFractiondsdtequals=f prime left parenthesis t right parenthesisf?(t) and the acceleration function ?a(t)equals=StartFraction d squared s Over dt squared EndFractiond2sdt2equals=f prime prime left parenthesis t right parenthesisf??(t)?, then complete parts? (a) through? (f). sequals=112112tminus?16 t squared16t2?, 0less than or equals?tless than or equals?77 ?(a heavy object fired straight up from? Earth's...
Consider this table of values for a function: x f(x) -3 15 -2 2 -1 -5...
Consider this table of values for a function: x f(x) -3 15 -2 2 -1 -5 0 -3 1 4 2 8 3 -12 How many zeroes does this function appear to have? Where are those zeroes (give intervals of x-values). Use interval notation. Can you be guaranteed that those are the only zeroes? Why or why not? If I told you that the table represented a third degree (cubic) polynomial, is that enough to guarantee that those are the...
Consider the function f(x)= tan 1/x Use the following table to guess the limit f(x) as...
Consider the function f(x)= tan 1/x Use the following table to guess the limit f(x) as x goes to 0+ x f(x) = tan 1/x 1/π 1/2π 1/3π 1/4π 1/5π 4/π 4/5π 4/9π 4/13π 4/17π
The table gives the average number of voters in a certain city in each of three...
The table gives the average number of voters in a certain city in each of three political parties during the last 12 years, along with the average number that voted in presidential elections during this period. Political Party Republican Democratic Independent Registered     voters 4500 6100 2200 Voted 2925 2379 1100 (a) For each political party, use these data to find the probability that a person selected at random from the registered voters in the party will vote in the next...
I want to to calculate the area between the x-axis and the function f(x) = sin(x)...
I want to to calculate the area between the x-axis and the function f(x) = sin(x) on the interval [0, pi]. The area we seek is enclosed in a rectangle bounded by the curves. x = 0, x = pi, y = 0, y = 1. Since we know the area of the rectangle is pi, we can generate random points inside the rectangle and keep track of how many of those points lie below the curve y = sin(x)....
. Assume a continuous function f(x) defined on x axis with a uniform grid spacing of...
. Assume a continuous function f(x) defined on x axis with a uniform grid spacing of h. The first and second derivatives of function can be approximated using information at more grid points giving rise to higher-order approximations. Using appropriate Taylor series expansions about location x, find the leading order truncation terms for the following approximations. Also indicate the order of accuracy for each approximation. Show all steps and box the final answers. Note: Look for the location at which...
Find a possible formula for the trigonometric function whose values are in the following table. x...
Find a possible formula for the trigonometric function whose values are in the following table. x 0 2 4 6 8 10 12 y 8 2 -4 2 8 2 -4 y =
Find a possible formula for the trigonometric function whose values are in the following table. x...
Find a possible formula for the trigonometric function whose values are in the following table. x 0 4 8 12 16 20 24 y 8 4 0 4 8 4 0
If a function f(x) is odd about a point, say (a,0), on the x-axis what exactly...
If a function f(x) is odd about a point, say (a,0), on the x-axis what exactly does this mean? How would you relate f(x values to left of a) to f(x values to right of a)? Similarly, if a function f(x) is even about a point, say (a,0), on the x-axis what exactly does this mean? How would you relate f(x values to left of a) to f(x values to right of a)? I understand what is meant by odd...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT