Divide the closed interval [2,6]\left\lbrack2,6\right\rbrack into 44 subintervals. What is the width Δx\Delta{x} of each subinterval? Write down all the grid points x0x_0, x1x_1, x2x_2, x3x_3, and x4x_4. If you need a left Riemann sum on this partition, which of those points do you use as sample points?

Δx=1\Delta{x}=1x0=2x_0=2, x1=3x_1=3, x2=4x_2=4, x3=5x_3=5, x4=6x_4=6Sample points: 22, 33, 44, 55

Δx=1\Delta{x}=1x0=2x_0=2, x1=3x_1=3, x2=4x_2=4, x3=5x_3=5, x4=6x_4=6Sample points: 33, 44, 55, 66

Δx=1\Delta{x}=1x0=2.5x_0=2.5, x1=3.5x_1=3.5, x2=4.5x_2=4.5, x3=5.5x_3=5.5, x4=6.5x_4=6.5Sample points: 2.52.5, 3.53.5, 4.54.5, 5.55.5

Δx=2\Delta{x}=2x0=2.5x_0=2.5, x1=3.5x_1=3.5, x2=4.5x_2=4.5, x3=5.5x_3=5.5, x4=6.5x_4=6.5Sample points: 3.53.5, 4.54.5, 5.55.5, 6.56.5

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Problem 49Multiple Choice

Divide the closed interval $open bracket 2 comma 6 close bracket$ into $4$ subintervals. What is the width $Δ x$ of each subinterval? Write down all the grid points $x sub 0$ , $x sub 1$ , $x sub 2$ , $x sub 3$ , and $x sub 4$ . If you need a left Riemann sum on this partition, which of those points do you use as sample points?

$triangle x equals 1$

$x sub 0 equals 2$ , $x sub 1 equals 3$ , $x sub 2 equals 4$ , $x sub 3 equals 5$ , $x sub 4 equals 6$

Sample points: $2$ , $3$ , $4$ , $5$

$triangle x equals 1$

$x sub 0 equals 2$ , $x sub 1 equals 3$ , $x sub 2 equals 4$ , $x sub 3 equals 5$ , $x sub 4 equals 6$

Sample points: $3$ , $4$ , $5$ , $6$

$triangle x equals 1$

$x sub 0 equals 2.5$ , $x sub 1 equals 3.5$ , $x sub 2 equals 4.5$ , $x sub 3 equals 5.5$ , $x sub 4 equals 6.5$

Sample points: $2.5$ , $3.5$ , $4.5$ , $5.5$

$triangle x equals 2$

$x sub 0 equals 2.5$ , $x sub 1 equals 3.5$ , $x sub 2 equals 4.5$ , $x sub 3 equals 5.5$ , $x sub 4 equals 6.5$

Sample points: $3.5$ , $4.5$ , $5.5$ , $6.5$

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