Directions: Briefly answer the reflection questions below. 1. Why do we need not to include the arbitrary constant C when evaluating a definite integral using the fundamental theorem of calculus? 2. Using the FTOC, evaluate the definite integral of the given function f2²(3x² – 2x)dx.

Q: Given P(A^c-complement)=0.40, P(B) =0.40, P(AUB)=0.75, P(A)= 0.60, P(B^c)=0.75 Find P((AnB)^c)

A: Additional Law of Probability gives P( A ∪ B ) =P(A) + P(B) - P(A∩B)

Q: lim x → +∞ [5x+2]] X

A: Solution :-

Q: Can the graph G be orientable? G:

A: Yes the graph is orientable.

Q: x Which of the following statements is/are true about the graph of R(x) = x² 4 - A. As the value of…

A: Introduction: For a rational function, vertical asymptote is quite natural. The points where the…

Q: ) Solve by using Laplace transform the partial differential equation ay-9 0² =0 dy(x,0) y(0,t)= 0,…

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Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

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Q: Establish the following set theoretic relations: a) AUB=BUA, ANB=BnA (Commutativity) b) AU (BUC) =…

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Q: Find the Laplace transform of t², -8 + 3t, 2. g(t) = - 6)² + 2 cos cos (1-2), 6 0 2

A: given g(t) is defined in (0,2)

Q: The Grinch sneaks into a room with 11 Christmas presents to 11 different people. He proceeds to…

A: consider the given question: Find the number of ways if no present is allowed to end up with its…

Q: Q3: Find f(t) (Inverse Laplace Transform )of the following functions nn 1. F(s) = 2.F(s) = s+1 s4+5²…

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Q: Consider a triangle ABC, on each of whose sides equilateral triangles are dra

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Q: given parameters a,b > o and the given sequence x₁= b X = n+1 4 (x₂ + 4a) n Xn a. Show that a b.…

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Q: 20) If y = a e/, then radius of curvature p = a sec² 0 cosec 0, if (a) 0 = tan-12 (b) 0 = tan ay -1…

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Q: x(n)= a"u(k − n) for k>0

A: Introduction: The Z-transform translates a discrete-time signal, which is a sequence of real or…

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: The demand function for an entrepreneur's product is given by p = q² - 5q + 119970 and the average…

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Q: Hiwo- solve the hyperblic partial differential equation numericaly where d²u d²u dx² = with initial…

A: Given  ∂2u∂x2=∂2u∂t2 The wave equation is ∂2u∂t2=c2∂2u∂x2 So c2=1 The difference for the given…

Q: ) Find the closures of the following sets:     Q, the set of rational numbers   2) Show that the…

A: Solution

Q: Use substitution to find the Taylor series at x = 0 of the function In 1 + 4x8 What is the general…

A: We have to find Taylor series for function in 1+4x8

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: so that the vector V = (x+3y)i + (y-2z)j + (x+az)k is solenoidal.

A: Solution :-

Q: Evaluate the following: (Note: Final answer should be expressed as a decimal, not in terms of gamma…

A: here we will use incomplete gama function and value of

Q: (a) Consider the feasible region in R² shown below (the red shaded region). 10 x+y=8 x+y=2 -3x - y =…

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Q: Find 2x2 matrices, A and B, such that AB = 0, but BA is NOT EQUAL to 0.

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Q: 2. Consider the following table. X₁ 0.2 0.3 0.6 0.9 1.1 1.4 1.6 1.3. 1.097 1.5698 Y₁ 0.050 0.098…

A: As per policy, we are allowed to answer only one question at time. So, I answering first question…

Q: 3. Express the given integral as the limit of a Riemann sum but do not evaluate: So (x³ - 6x) dx.

A: Solution:-

Q: Consider the curve defined by the equation y = 5x + 1x. Set up an integral that represents the…

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Q: Find what value of c does f&dx = 1? с Answer:

A: Solution

Q: an= (-5)n an an = COS 4n+n3 3n+4" os(T) 8

A: The detailed solution with explanation is presented as the next step.

Q: Consider the function. + 10 f(x) = Determine the intervals on which f is increasing, decreasing,…

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Q: If A, B, C are sets, show that a) A x B= 0 ⇒ A=0 or B = 0. b) (AUB) x C = (AXC) U (BxX C). c) (An B)…

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Q: Be sure to show all work and all problem solving strategies. Give complete explanations for each…

A: Solution : a) X1 matrix is product of A and X where, X1(i,1)=Ai1X0(11)+Ai2X0(21)+Ai3X0(31) where,…

Q: region (levels: Northeast, North Central, South, and West) whether the respondent feels things in…

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Q: u)n(p+u°О

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Q: 7. Evaluate the integral x4 6x5 1 dx

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Q: If z₁ = 13-101 and 22-15 +91, determine the following: 42₁-522 (Polar Form) COMPLETE THE MISSING THE…

A: We have z1=13-10i , z2=-15+9i Consider: 4z1-5z2=413-10i-5-15+9i=52-40i+75-45i=127-85i Hence,…

Q: (ylny – e¯xy)dx + ( + xlny) dy = 0

A: Solution :-

Q: Let X be a limit point compact metrizable space. (a) Show that there exists no continuous,…

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Q: Q3) A building was photographed using an aerial camera from a flying height of 1000 m. The photo…

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Q: owing assertion: n

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Q: Solve: y' + 4y - 17y' - 60y: = y(0) = - 4, y'(0) = - -5, y(t) = = - 72et y''(0) = - 65

A: First we will find the Auxiliary equation of given differential equation to get Complementry…

Q: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

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Q: 3. Use a midpoint Riemann sum with n = 300 to approximate (22³ – 8)dr. Round your answer to -2 four…

A: we are to divide the interval with length ∆x =0.023333333333333 So  the data points are…

Q: Q4:- if you know that data ( 12, 10,12,10, 10,6) find the :- Mode, median, mean, variance and…

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Q: If 11z¹ +10iz⁹ +10 iz-11 = 0, find the possible values of [z].

A: The given question is related with complex analysis. Given the equation 11z10 + 10iz9 + 10iz - 11 =…

Q: Use substitution to find the Taylor series at x = 0 of the function 14 sin (-x). What is the general…

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Q: Let f, g be two functions defined from R into R. Translate using quantifiers the following…

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Q: z+y <=0. (a) Using - definition, show that lim (a)+(0,0) 2²+ y² +1 [2²sin +3² sin, (2, 3) (0,0) (b)…

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Q: Let (l, m, n,), i = 1, 2, 3 be the direction cosines of 3 mutually perpendicular lines. Find the…

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Q: POMERO OF 10 al rate of 0.9% compounded continuously, how long to the nearest year) would take b the…

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