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Fed [463]
3 years ago
9

Find f if f′(x)=2x−3/x^4, x>0 and f(1)=2.

Mathematics
1 answer:
slavikrds [6]3 years ago
8 0
f'(x)=2x-\dfrac3{x^4}
\displaystyle\int f'(x)\,\mathrm dx=\int\left(2x-\frac3{x^4}\right)\,\mathrm dx
f(x)=x^2+\dfrac1{x^3}+C

Given that f(1)=2, we get

2=1^2+\dfrac1{1^3}+C
2=2+C
\implies C=2

so that

f(x)=x^2+\dfrac1{x^3}
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One less than five times a number is fewer than twenty-four
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Ad libitum [116K]

The area of the composite figure can be found by summing the whole area that made up the figure. Therefore, the area of the figure is 213.5m²

<h3>Area of a composite figure</h3>

The area of the composite figure is the sum of the area of the whole figure.

Therefore, the composite figure can be divided into 2 triangles and two rectangles.

Hence,

area of triangle1 = 1 / 2 × 10 × 13 = 65 m²

area of the triangle2 = 1 / 2 × 15 × 7 = 52.5 m²

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area of rectangle3 = 5 × 6 = 30 m²

Therefore,

area of the composite figure = 65 + 52.5 + 24 + 42 + 30 = 213.5 meters squared

learn more on area here: brainly.com/question/27744042

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8 0
2 years ago
Write the first five terms of a geometric sequence in which the sixth term is 64.
azamat

Answer:

1st term : 2

2nd term : 4

3rd term: 8

4th term : 16

5th term : 32

Step-by-step explanation:

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16.058−1.2

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7 0
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