Let F X X 7 2 5 Classify The Point 7 F 7

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Let f (x) = (x – 7)2/5 , classify the point ( 7 , f (7)).

a)vertical cusp

b) local maximum

c) vertical asymptote

d)horizontal asymptote

e) vertical tangent

f) inflection point

g) none of these

i did vertical tangent but its incorrect

 
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Let F X X 2 Sin 1 X For X Not 0 And F 0 0 A Observe F Is Continuous On R See Exe

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Let f(x)=x^2*sin(1/x) for x not=0 and f(0)=0. 

(a) Observe f is continuous on R; see Exercises 17.3(f) and 17.9(c).

(b) Why is f uniformly continuous on any bounded subset of R?

(c) Is f uniformly continuous on R?

 
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Let F X X3 X 1 And 30 X3 X2 2x 1 Find The Area A Of The Bounded Region Between T

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10. 11. 12. Let f(x) = x3 + x — 1 and 30:) = x3 — x2 + 2x + 1. Find the area A of thebounded region between the graphs offand g. (10 pts) Consider the graph of the curve with parametric equations x(t) = —3 sin(2t),y(t) = 4cos(2t), for t 2 0. a. Sketch the graph of the curve, and indicate the direction of increasing t. (Lookingahead to part c might be helpful.) (5 pts) b. Find the slope of the line tangent to the graph of this curve when t = E. No approximations. Find 2—: n by using the formula in the box of section 2.2, p. 169.t:—6(5 NS)2 2c. Show that x? + {—6 = 1. A curve with this equation is called an (fill in theblank). (5 pts) d. By using implicit differentiation on the equation in part c), find 2—: in terms ofxand y. Calculate x (E) and y (E), and reconcile your answer to part b). (5 pts) Consider the function f(x) = i lnx’a. Determine the domain off. (5 pts)b. Find the vertical asymptote(s), if any, of this function. Use limits to justify thatyou have in fact found the asymptote(s). (5 pts) c. Find the horizontal asymptote(s), if any, of this function. Use limits to justify thatyou have in fact found the asymptotes. (5 pts)

 
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Let F X Y X2y22y 1 Be Subject To The Constraint X2 Y2 4 A Find All Candidate Poi

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 Let f(x,y)=x2−y2−2y+1 be subject to the constraint x2+y2 ≤4.

(a) Find all candidate points for the locations of the absolute extrema lying

inside the region given by x2 + y2 ≤ 4. 

(b) Using the method of Lagrange multipliers, find all candidate points for absolute extreme along the boundary of the region given by x2 + y2 ≤ 4. 

(c) Using your answers above, what are the absolute maximum and absolute minimum values of f over the given region? Clearly label and circle the absolute extrema (give the exact function values, not the locations of the extrema). 

 
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Let Follow An Exponential Distribution With Rate Parameter Amp 2 Let I Follow A

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This is a statistics question. We need to use RStudio to get the answer of this question. Therefore, this is actually an coding problem in R

Let * follow an exponential distribution with rate parameter &* = 2. Let I" follow a Poisson distributionwith rate parameter^` = $.We write sall I ; for the true standard deviation of I and mall"; for the true median of I".Let s _ he the sample standard deviation of I which is an estimate of sillly. Also let my he the samplemedian which is an Estimate of mill’ ] .Suppose we take samples of size `= = 101 from* and take samples of size my = ]. Consider the statisticWhat is the ( sampling ; distribution of* ! We could ask a statistician who specializes in theary . Instead oflising mathematics . simulate* Good times and stare the results . Plot a histogram of the observed values ofAL . Comment on the shape of the histogram and empirical distribution of* . Before running your code , Set.the same seed used for the previous exercise . For full credit , do not use a For Long.

 
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Let Fp Denote The Field Z Pz For P A Prime And Consider The Ring Fp X Of Polynom

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Let Fp denote the field Z/pZ for p a prime, and consider the ring Fp[x] of polynomials with coefficientsin Fp. We say that two polynomials g(x), h(x) are congruent modulo f(x) if f(x) divides g(x) − h(x)in Fp[x], i.e., there exists a polynomial q(x) in Fp[x] so that f(x)q(x) = g(x) − h(x). Now let p = 2 andlet f(x) = x2 + x + 1 and g(x) = x. Find a polynomial h(x) so that g(x)h(x) is congruent to 1 modulof(x). (You can do this by trial and error because this is a simple example, but you can also use theanalogue of the Euclidean algorithm for polynomials if you wish.)

 
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Let G Be A Connected Bipartite Graph I E The Set Of Vertices Is Split As X S Y S

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Let G be a connected bipartite graph (i.e the set of vertices is split as X S Y so that the edges are connecting some pairs xi ∈ X with yj ∈ Y ). Show that if each vertex has multyplicity 3 then there is a complete matching( i.e the number of vertices in X is the same as in Y and there is matching of all vertices in X with vertices in Y )

 
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Let G Be A Directed Acyclic Graph Dag With N Vertices And M Edges

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  1. Let G be a directed acyclic graph (DAG) with n vertices and m edges. Give an O(n + m)-time algorithm, that takes as input an ordering of the n vertices of G, and checks whether or not this ordering is a topological sorting for G.
 
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Let G Be A Group Of Order 42 A Prove That G Has A Normal Subgroup Of Order 7 B P

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Let G be a group of order 42.

Prove both (a) and (b).

Prove both (a) and (b).

Prove both (a) and (b).

7 . Let G be a group of order 42 .( a ) Prove that G has a normal subgroup of order 7 .`( b ) Prove that G is a semidirect product of a normal subgroup of order 21 and 2.2 .

 
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Let G Be The Prisoners Dilemma Game With Stage Payoffs

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Let G be the Prisoners Dilemma  game with stage payoffs:

CDC2,20,3D3,01,1

Find the values of δ ε(0, 1) such that the tit-for-tat strategy can be sustained as a SPNE in the infinitely repeated PD G(infinity, 1)

 
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