Calculate S30 for the arithmetic sequence defined by {an}={3.1n-2}

Mathematics

1 answer:

timurjin [86]2 years ago

3 0

Answer:

c) 1,381.5.

Step-by-step explanation:

First term = 3.1 *1 - 2 = 1.1

2nd term = 3.1*2 - 2 = 4.2

3rd term = 3.1*3 - 2 = 7.3

so the common difference d = 3.1.

S30 = (30/2) [ 2* 1.1 + (30-1) * 3.1)]

= 1,381.5.

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Using a linear approximation, estimate f(2.1), given that f(2) = 5 and f'(x) = √3x-1.

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Answer:

$f\left( {2.1} \right) \approx 5.22360$ .

Step-by-step explanation:

The linear approximation is given by the equation

${f\left( x \right) \approx L\left( x \right) }={ f\left( a \right) + f^\prime\left( a \right)\left( {x - a} \right).}$

Linear approximation is a good way to approximate values of $f(x)$ as long as you stay close to the point $x= a$ , but the farther you get from $x=a$ , the worse your approximation.