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DiKsa [7]
2 years ago
11

9.) Find the following antiderivative

Mathematics
2 answers:
Studentka2010 [4]2 years ago
8 0
◆ Indefinite Integration ◆

IrinaVladis [17]2 years ago
5 0

Let u = 5x+1. Then du = 5·dx, and your integral is

\displaystyle\frac{1}{5}\int{\frac{5}{5x+1}}\, dx=\frac{1}{5}\int{\frac{1}{u}} \, du}\\\\ =\frac{1}{5}\ln(u)=\frac{1}{5}\ln(5x+1)

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30 pts + BRAINLIEST
ivanzaharov [21]

Answer:

Number of permutations = 5040

Step-by-step explanation:

We are given the word 'INNOVATIVE', that has total 10 letters.

Now, we are asked to form words using exactly 4 letters at a time i.e. out of 10 letters we are using 4.

Therefore, the number of permutations that can be formed using 4 letters are = P(10,4)

i.e. 10_{P_{4} }

= \frac{10!}{(10-4)!}

= \frac{10!}{6!}

= \frac{10*9*8*7*6!}{6!}

= 10*9*8*7

= 5040

8 0
3 years ago
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The graph of f ′ (x), the derivative of f(x), is continuous for all x and consists of five line segments as shown below. Given f
Nataliya [291]

The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.

Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.

By the fundamental theorem of calculus,

\displaystyle f(5) = f(0) + \int_0^5 f'(x) \, dx

The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so

\displaystyle \int_0^5 f'(x) \, dx = \frac{5+2}2 \times 2 = 7

\implies \max\{f(x) \mid 0\le x \le5\} = f(5) = f(0) + 7 = \boxed{13}

8 0
2 years ago
Please help! I will give brainlest answer
Sidana [21]
Connect the bdc letters together.
8 0
3 years ago
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Customers can pick their own blueberries at blueberry hill. They pay $5 to enter the patch and $4 per round for the blueberries
Pavlova-9 [17]
Y=5+4x 
Because it is 5 dollars when you enter and then 4 dollars per round

5 0
3 years ago
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What is the next term of the arithmetic sequence 1, -2, -5, -8, ...
Vaselesa [24]

Answer:

-11

Step-by-step explanation:

Subtract 3 everytime

3 0
2 years ago
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