Mathematics, 31.10.2020 20:10 itsyogirl12

Estimate the area under the graph of f(x)=x^(2)+3x from x=1 to x=5 using 4 approximating rectangles and left endpoints.

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Answer from: daniel9299

Rn ≈ 0.6345

Ln ≈ 0.7595

Step-by-step explanation:

The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.

It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:

x = -1, -.25, 0.50, 1.25, 2

Of course, the spreadsheet can easily compute the sum of products for you.

The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:

Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)

Rn ≈ 0.6345

The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:

Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)

Ln ≈ 0.7595

It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).

Step-by-step explanation:

Rn ≈ 0.6345

Ln ≈ 0.7595

Step-by-step explanation:

The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.

It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:

x = -1, -.25, 0.50, 1.25, 2

Of course, the spreadsheet can easily compute the sum of products for you.

The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:

Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)

Rn ≈ 0.6345

The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:

Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)

Ln ≈ 0.7595

It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).

Answer from: Quest

The answer is c because you turn 17.5% into a decimal which gives you .175 then you times that by $361.35 which gives you 63.23625 but then you round that which gives you 63.24. then you at 63.24 pulse 361.35 and you round it which gives you $425

Answer from: Quest

i do not know this sorry : (

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Estimate the area under the graph of f(x)=x^(2)+3x from x=1 to x=5 using 4 approximating rectangles...

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