Find the limit when X approaches zero
2xsinx/1-cosx

Answer:

4

Step-by-step explanation:

[tex] Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1^2 -\cos^2 x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1 -\cos^2 x} [/tex]

[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{sin^2 x} [/tex]

[tex] =Lim_{x \to 0}\frac{2x(1+\cos x) }{sin x} [/tex]

[tex] =Lim_{x \to 0} 2(1+\cos x) \times \frac{1}{Lim_{x \to 0}\frac{sin x}{x}} [/tex]

[tex] =2(1+\cos 0) \times 1 [/tex]

[tex] = 2(1+1) [/tex]

[tex] = 2(2) [/tex]

[tex] \therefore Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}= 4 [/tex]

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Use the table to answer the question. The table shows the results of simulating this situation using a random number generator.
The numbers 0 to 6 represent a win on the home court, and 7 to 9 represent a loss on the home court.

479  787  293  926  807 398  730  994  718  184 978  400  904  488  508 241  729  673  178  982 556  355  137  241  430 500  379  811  147  260 250  704  631  109  287 172  870  124  557  192 803  588  674  856  678 385  981  830  972  949

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Type your answer into the box.
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