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Question: (Continuation of Problem) You may remember that the Second Derivative test tells us nothing when the second derivative is zero at the critical point. In this problem you will investigate that special case. Assume g has the same properties as in Problem 54, and that, in addition, g"(0) = 0. What does the Taylor polynomial tell you about whether g has a local maximum or minimum at x = 0?
Problem: All the derivatives of g exist at x = 0 and g has a critical point at x = 0.
(a) Write the nth Taylor polynomial for g at x = 0.
(b) What does the Second Derivative test for local maxima and minima say?
(c) Use the Taylor polynomial to explain why the Second Derivative test works.
For the series n=1Σ∞1, find a formula for the partial sums SN, the limits limn→∞ an and limN→∞ SN, and determine whether the series converges or diverges.
Use the Theorem of Pappus to find the volume of the solid obtained by rotating the triangle with vertices (5, 4), (5, 8), and (11, 6) about the x-axis.
In order to understand the causal relationship in business process, manager often asks "whys" to drill down the root cause of failures. Select one (1) project from your working or educational environment and propose at least three (3) "why" questi..
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Find the eigenvalues and eigenvectors.
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A linear polynomial P(x) and a quadratic polynomial Q(x) such that the rational function P(x)/Q(x) does not have a partial fraction decomposition of the form.
Show that the relation of logical equivalence on the set of all compound propositions is an equivalence relation. What are the equivalence classes of F and of T?
Find the resultant (sum) of the complex numbers. Express in rectangular form
Think of the success story for a time when you were part of a team and you accomplished the goal or created the constructive change you set out to make happen. Share your story and answer the following questions in a 200-250 word discussion:
Find the standard deviation of the data in the given frequency table. A company had 80 employees whose salaries are summarized in the frequency table below. Find the standard deviation.
For a certain laser device, the laser output power (in mW) is negligible if the drive current is less than 80 mA. From 80 mA to 140 mA.
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