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Margaret [11]
2 years ago
13

Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) f(x) = x/(x^2 + x + 3

)

Mathematics
1 answer:
xz_007 [3.2K]2 years ago
3 0

Answer:

Follows are the solution to this question:

Step-by-step explanation:

In the given function, its denominator value that is x²+x+3 is always given a positive value.

This function has a polynomial expression in the numerator and denominator value, that's why the above the function is defined everywhere in the interval value.

please find the attached file.

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7nadin3 [17]
So we can get from these two equations that y = 6x + 2 = 6x + 9

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Answer:

77.  \cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} xProved

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Step-by-step explanation:

77. Left hand side

= \cot^{6} x

= \cot^{4} x \times \cot^{2} x

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{Since we know, \csc^{2} x - \cot^{2}x = 1}

= \cot^{4} x \csc^{2}x - \cot^{4} x  

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78. Left hand side

= \sec^{4}x \tan^{2} x

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{Since \sec^{2}x - \tan^{2}x = 1}

= \sec^{2}x [\tan^{2}x + \tan^{4}x ]

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79. Left hand side  

= \cos^{3} x\sin^{2} x

= \cos x[1 - \sin^{2} x] \sin^{2} x

{Since \sin^{2}x + \cos^{2} x = 1}

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{Since \sin^{2}x + \cos^{2} x = 1}

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