Suppose that f(5) = 1, f '(5) = 4, g(5) = -8, and g'(5) = 2. Find the following values. (a) (fg)'(5) (b) (f/g)'(5) (c) (g/f)'(5)

Q: g(x) = 2 5x-6

A: I have solved the problem step by step

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A: Take r3 common from numerator and denominator and then use the limit.

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A: We need to find limit.

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A: All parts of the given problem is solved below in detail.

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A: Given that: To divide 1×1010 by 5×10-20

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A: Use Definition of limits to calculate f'(-3)

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A: We can find the numerical value by taking partial derivative of the function with respect to 'x'…

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A: We can solve this as follows:

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A: Please refer to the image below

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A: Follow the procedure given below.

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A: Given :A-1=-0.20.30.4-0.1

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A: We can solve it by general form of parabola as follows

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A: Find second derivative  Solution is done in step 2

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Q: 49. Find an equation of the line tangent to the graph of y = √x/(x + 1) at (a) x = 1; (b) x = 1.

A: We need to find equation of tangent.

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A: Given that…

Q: If   3x − 1 ≤ f(x) ≤ x2 − 3x + 8   for  x ≥ 0,  find   lim x→3 f(x).

A: Apply limits to the inequality

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A: The graph of fx is shown below. To estimate and to list the values of x where fx has a horizintal…

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A: We know that 1/infinity tends to 0

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Q: Find the arc length of x=r cost, y=rsint 0≤t≤2T

A: