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Monica [59]
4 years ago
13

the 20th term of an arithmetic sequence is 98, and the common difference is 6. Determine the 63nd term.

Mathematics
1 answer:
lina2011 [118]4 years ago
8 0
The 63nd term is 356 i beleve
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Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by
elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate x^4.

We have

\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h

Expand the numerator using the binomial theorem, then simplify and compute the limit.

\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}

In general, the derivative of a power function f(x) = x^n is \frac{df}{dx} = nx^{n-1}. (This is the aptly-named "power rule" for differentiation.)

3 0
2 years ago
HELP DUE TOMORROW ANSWER ALL FOUR PARTS PLZ
NikAS [45]

Answer:

7. A

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How many minutes are there in 12 hours? Why would the vertical translation (D) be a number that is close to this value?
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Step-by-step explanation:

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o-na [289]

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If in two minutes 125 people enter the park, then in 1 minute 75 people enter the park. For it ti be linear, in 3 minutes  225 would have to had entered the park, and in 4 minutes 300, 5 minutes 375.

5 0
3 years ago
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