***please show full work! This is very very urgent! Thanks!! If f(x) is continuo

Question

***please show full work!

This is very very urgent!

Thanks!!

If f(x) is continuous at x = -7, which of the following statements is true? f(x) = f(-7) -f(x) does not exist f(x) does not exist f(x) = f(7) f(x) = -7 Find the derivative with respect to x of the following using implicit differentiation. x9y9 + x8 sin (y) = 10 dy/dx = 1/81x8y8 + 8x7 cos (y) dy/dx = -9xy9 - 8sin (y)/9x2y8 - x cos (y) Which of the following describes the following function at c = 37? f(x) = x/x-4 The function is discontinuous at c = 37 because f(c) does not exist. The function is continuous and discontinuous at c = 37. The function is continuous at c = 37. The function is discontinuous at c = 37 because the limit of f(x) as x approaches c does not exists The function is discontinuous at c = 37 because f(c) does not equal the limit of f(x) as x approaches c.

Explanation / Answer

12. Given that function is coninuous at x=-7.

it means that value of left hand limit is equal to value of right hand limit is equal to value of function at x=-7.

So, option A is correct.

13. Differentiating with respect to x,

9x^8 y^9 + x^9*9y^8 * dy/dx + 8x^7sin y + x^8cos y dy/dx = 0

taking coefficient of dy/dx one side

dy/dt(x^9*9y^8 + x^8 cos y) = -(9x^8y^9 +8x^7 siny)

dy/dx = -(9xy^9 + 8siny)/(9x^2y^8 + xcos y)

B is correct

14. as limit x tends to 37 f(x)

by plug in x=37, we get f(x) = 37/33

as it is finite value.

So, function is continuous at c=37

And hence c is correct answer.

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