. Rolle's Theorem: Assume f has a derivative (finite or infinite) at each point of an open interval (a,b), and assume that f is continuous at both endpoints a and b. If f(a) = f(b) there is at least one interior point c at which f'(c) = 0.

Q: notice that the ci cle e a cherd sL a ar ele u a line me wtate se gmni corne etıng iuo pents Jo pick…

A: Q1) The CDF for r here is obtained as:F(r) = P(R <= r) As the point is uniformly distributed over…

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A: Follow the steps.

Q: a2 b2 C2 If Aj = [di ei fi] A2 = [d2 e2 2] real numbers, show that: 9. (A, +A,) + Az = A, + (A, +A3)

A: # As per the guidelines we are entitled to solve one question at  a time ,please resubmit the other…

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A: Given, t(s) 0 12 24 36 48 60 v(ft/s) 32 28 24 22 24 28

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Q: 11. Given f(x) = e*. (a) Complete the following table. 0.25 0.75 1.0 f(x) = e* (b) Hence, find P,…

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Q: {15n : п € Z} %3 {3п :п€ Z}n{5n :n€ Z}

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A: Given that y'=2xy+x2ex, 1≤x≤2, y2=0 with exact solution yx=x2ex-e

Q: 5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x ,y 4.

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Q: 1. Eliminate the arbitrary constants on the given equation: y=Ae^x+Bxe^x

A: Formation of the differential equation, by elemination of the arbitrary constants

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Q: Q2/ Fit a second - order polynomial to the data in the following table: 5 1 4 2 9 Y 8. 4 -1 8 4 6 6…

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Q: . Let f : [0, 1] R be defined by |-1, z = ; >50 f(x) = {0 |<a < }; 1, 21 (a) Show that f € R([0,…

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Q: line re gment corine tin g tuo pents pick a peut in the unit ciscle that are randomdy unit a a cherd…

A: The CDF for r here is obtained as:F(r) = P(R &lt;= r) As the point is uniformly distributed over the…

Q: c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

A: To find complex no. in standard form using De Moivre's theorem .