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enyata [817]
4 years ago
14

HELP! PLEASE! which graph represents a function? How do you know?

Mathematics
2 answers:
Andreas93 [3]4 years ago
5 0
I agree the answer is D
WITCHER [35]4 years ago
4 0

Any graph will represent a function if it passes the vertical line test. A graph is a function if for any vertical line drawn it touches the graph at only one point.In other  words for every x there is only one y value.

In the given graphs if a vertical line is drawn in the graphs A,B it will touch the graph at two points and hence they are not unctions.Option c s a vertical line that is for one x value there are more than one value of y and so is not a function.Option D will represent a function as any vertical line drawn will touch the graph at only one point.

OPtion D.

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Arisa [49]

Answer: S_n=5(1-\dfrac{1}{n+1}) ; 5

Step-by-step explanation:

Given series : [\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]

Sum of series = S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]

Consider \dfrac{1}{n\cdot(n+1)}=\dfrac{n+1-n}{n(n+1)}

=\dfrac{1}{n}-\dfrac{1}{n+1}

⇒ S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]

Put values of n= 1,2,3,4,5,.....n

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All terms get cancel but First and last terms left behind.

⇒ S_n=5(1-\dfrac{1}{n+1})

Formula for the nth partial sum of the series :

S_n=5(1-\dfrac{1}{n+1})

Also, \lim_{n \to \infty} S_n = 5(1-\dfrac{1}{n+1})

=5(1-\dfrac{1}{\infty})\\\\=5(1-0)=5

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