Integrate the following: 3 1 x2-x3 (a) (b) 12x4 - dx [ (x2-02) a2); dx

Q: 2 If $ fcx If f f(x) dx = 5 then and I f (3x-1) dx = ? I 2 5 f(x) dx = 39

A: We are given two definite integrals : ∫12 f(x) dx = 5   ,   ∫25 f(x) dx = 39 Now using these we have…

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Q: 34. Let A = -[- the set of all linear combinations of the columns of A. 2 0 8 1-2 6 5 1 10 -[19]. ['…

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Q: 3. By finding a suitable integrating factor, solve the following equations: (a)…

A: (a)  Given DE is  1-x2 y'+2xy = 1-x232                    ⇒  y'+2x1-x2y= 1-x2           This is…

Q: (c) lim x² 2 4 x⇒-2 x -2 Calculate the following limits, or explain why they diverge. (d) lim x² + 4…

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Q: Q3: A particle traveling in a straight line is located at the point (1,-1,2) and has speed 2 at time…

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Q: Find the solution of the differential equatic 4 y² + y = x³y² y (2)= X

A: Given ODE y'+4xy=x3y2, y(2)=-1 which can be written as  y'y2+4x1y=x3

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Q: A 45 foot tall telephone mast r feet from an observer subtends an angle of 1.75°.

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Q: Write a system of equations that is equivalent to the given vector equation C-8-68 I1 4 -5

A: Given that the vector equation x14-5+x274+x3-41=00  .

Q: Prove by induction on n, that for all real x ER with sin(x) #0 we have sin(2nx) cos(x) + cos(3x) +…

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Q: Exercise 0.3.11: Prove by induction that n < 2n for every natural number n. Remarks Recall from Math…

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Q: Inner Product and Length of Vectors and Distance in IR² and IR³. If a,be IR³, then their product or…

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Q: Consider the pair of two-dimensional systems 0 = (-22) X and Y' = 0 X' = (83) Y. (b) Find a…

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Q: 3. y" + k²y = f(x) with boundary conditions y (0) = 0 and y(L) = 0

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Q: Simplify, then evaluate without using a calculator. 2 c) ›(()) a) b) () ()* OY, 2031 d) ›('()' - (*…

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Q: Find the limit. NOTE: Enter the answer using round brackets. lim t+∞ t² +8 1 5t² + 6' t (?, ?)

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Q: C. Find the complete solution of the d.e. y" - 5y' + 4y = 8e*, y = y + Yp using Exponential shift

A: Given differential equation y''-5y'+4y=8exD2y-5Dy+4y=8exD2-5D+4y=8ex

Q: Let d be a trivial metric on a non-empty set X and d₁: XXX → R such that x = y d₁(x,y) = { 2 if x…

A: Given:d1:X×X→R such that  d1x, y=0if x=y2if x≠y∀x , y∈X To Show: d and d1 are equivalent.

Q: Problem 1: Trees Consider the tree above: [a] What kind of tree is it? 1 [i] What is its postorder…

A: (g) A complete tree is the one in which every level except the last one is completely filled and the…

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Q: Jump to level 1 Fill in the missing numbers of the sequence generated by Euclid's algorithm on…

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Q: Find the length of the curve r = sin(0/3), 0≤0 ≤ 3π/2. The length of the polar curve is (Type an…

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Q: Evaluate the triple integral y dV where is the solid tetrahedon with vertices (0, 0, 0), (4, 0, 0),…

A: To Evaluate: ∭ExydV. Here E is the solid tetrahedron with vertices O0, 0, 0, P4, 0, 0, Q0, 6, 0, and…

Q: Describe how to reorder the terms in explain why no such reordering is possible. 8 n=1 (-1)" to add…

A: This comes from " Riemann’s Rearrangement Theorem " Riemann's  Rearrangement  Theorem :  Let ∑an be…

Q: cells of a clothing company decrease from 60,250 to 52,100 find the percent o

A: Given that the daily cells of a clothing company decrease from 60,250 to 52,100.

Q: Determine the truth value of each of these statements if the domain is R. Explain your answer.…

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Q: Given the equation 2xsin² ydx-(x² +10) cos ydy = 0, Find an implicit solution. Find the constant…

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Q: Sketch the graph of the function. F(x) if xs-1 if -1 2

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Q: Let f [0, 1] → C be continuous, and let g: C → R be continuous. : Show that g(f([0, 1])) is a closed…

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Q: ind the general solution to the following differential equations and determine how the solution y(t)…

A: dydt+3y=t+e-2t Its a linear differential equation, hence integrating factor e∫3dt=e3t

Q: An electronics company produces three models of stereo speaker, models A, B, and C, and can deliver…

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Q: 5. Consider the ODE (5x²y + 6x³y² + 4xy²)dx + (2x³ + 3x¹y + 3x²y)dy = = 0. (a) Show that the ODE is…

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Q: sin(1x) - 10

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Q: Find the list price of a desk that has a net cost of $153 after trade discount of 15/10

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Q: Find the general solution to the following Bernoulli Equations : 1) dy/dt + y = y^2 b) dy/dt + y =…

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Q: Mark purchase items at a grocery store the items total $42.89 before taxes after paying the NYC…

A: Mark purchase items at a grocery store, the items total $42.89 before taxes. Mark paying the NYC…

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Q: - (3) Show that for a, b € R we have a + b + |a − b] = 2 max{|a|, |b|}.

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Q: Determine the truth value of each of these statements if the domain is R. Explain your answer. 3.…

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Q: Linear algebra: please correctly and handwritten

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Q: Bisection and Regula falsi f(x)=x³+4x-3 with 6 iterations

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