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1. Let I ⊆R be an open interval. Let c ∈ I, let n ∈ N and let f1,....., fn: I→R be functions. Suppose that fi is differentiable at c for all I ∈ {1,....,n}. Prove that f1 f2.... Fn is differentiable at c, and find (and prove) a formula for (f1f2...fn)'(c) in terms of f1(c),....,fn(c) and f'1(c),...., f'n(c).
2. Let I ⊆R be an open interval. Let c ∈ I, let f, g:I→R be functions and let k ∈ R. Suppose that f and g are differentiable at c. Prove kf is differentiable at c and |kf|'(c) = kf'(c).
3. Explain the flaw in the proof in the attachment. Restate the Chain Rule with the proper with modified hypotheses that would make the attempted proof into a valid proof.
Attachment:- attachment.rar
The trigonometric function to find exact value.
Claire sells packets of sunflower seeds for $0.95 each and packets of morning glory seeds for $1.43 each. She decides to offer a 16-packet spring-garden combination, combining both types of seeds at $1.10 per packet.
The distance from a star to a planet is 3.1 * 1019 m. How long does it take light, traveling at 1016 m/year, to travel from the star to the planet?
Determine the value of the integral directly. the trapezoidal rule estimate for n = 4. an upper bound for |ET|. the upper bound for |ET| as a percentage of the integral's true value.
Calculate the surface area of an unopened steel can that has a height of 5cm and a radius of 7cm.
Solve the average cost function.
the area of a rectangle is 991cm squared. if 991 is a prime number what are the whole number dimentions of the rectangle?
to lay their eggs green turtlea travel hundreds of miles to the beach where they were born. the eggs are buried on the
1. Which type of ANOVA should you use to analyze these data, and why should you choose this type of ANOVA? 2. Analyze your data, being sure to interpret your results and explain your reasons for declaring them significant or not significant.
1. data from a national health survey show that mens average weight is normally distributed with a mean of 172 pounds
Determine an equation for the right bisector of the line segment with endpoints P(-5,-2) and Q(3,6)
What is the probability that a part that starts in Process A will make it to shipping in two steps? Show the values that you are combining to solve this.
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