O O 2x4 1,34 dx +1 NIS In[x5 + 1] + € C In[x5 + 1] + C 5 In[x 5 + 1] + C In[x5 + 1] + C

Q: The eigenvalues of a square matrix A are the numbers À for which the matrix A-XI is regular.

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Q: If R = {(x, y) : 0 ≤ x ≤ 1,0 ≤ y ≤ 1}, then find (²+1) +2 0 1 arctan O 2√2 3 0 √2 3 O √2 3 (√³/₂2)…

A: Please see the below picture for detailed solution.

Q: Find the domain of the vector-valued function given below. r(t) = √√16-t²i+ 1 t+6 j+(t−4)k

A: We have to find the domain of the vector-valued function rt = 16-t2i + 1t+6j + t-4k

Q: The traffic flow rate (cars per hour) across an intersection is r(t) 200+600t 120t², where t is in…

A: The traffic flow rate across an intersection is rt=200+600t-120t2, where t is in hours and t=0 is 6…

Q: Differentiate y = (2x³ + 3x² - 1)5 30x(x + 1)(2x³ + 3x² - 1) O 5(6x² + 6x)+ 30x(x+1)(2x³ + 3x² - 1)4…

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Q: a) z=x² In (x y²) b) z=4 cos(x-3y)

A: As we know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Chain rule:…

Q: Find the total area of the shaded region. 1.5- 1- 0.5- 0 y x=12y³ 6 x=12y² (12,1) 12 18

A: The equation of the curves are: x = 12y3 x = 12y2 The graph of the curves is To evaluate: The area…

Q: 9 == find f'(x) using the limit definition of the derivative. x Given f(x) = f'(x)=

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: f(x) = 2x^3 − 3x^2 − 18x − 8 Factor f(x) into linear factors. Don’t forget to include the leading…

A: Please see the below picture for detailed solution.

Q: 4 In the following differential equations, test for exactness and determine the solution of each: 1.…

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Q: Determine whether the series Σ=1 (Limit Comparison Test) 2n²+3n √5+n5 converges or diverges.

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Q: Given: f(t) = 3t4 + 6. Evaluate: F(3) Use 2 decimal places. 2.30

A: Here we have to apply laplace transform.

Q: Classify the given differential equation according to its type, order, degree, and linearity. d²y…

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Q: π f(x,y) = sin 3(x+y) over the square 0≤x≤60sys 6. R

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given that,            The solid is obtained by rotating the region bounded by the given curves…

Q: Evaluate 02 3√2 0 1 3√2 0 1 |- √2 1|2 sino 4cos0 LLL rdzdrd0.

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Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: n=1 n! n - (x − 3)" 2n

A: The series is given by ∑n=1∞n!2nx-3n To determine:  The radius of convergence. The interval of…

Q: 3x + 7 Consider the function f(x) = 4x + 1 and (A, ∞o) where the function is not defined at A. Find…

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Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Show the final answers using EXACT values only, not calculator-ba Show complete solutions. Evaluate…

A: solution given be;ow

Q: 6 5 4 3 a The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s)

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y+3y" - 3y - 2y = et,…

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Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…

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Q: Solve the given initial value problem. 0x²y² + xy³ = 2 0x²y² + y² = 3 ○ xy² + xy³ = 0 Oxy²y³ = 1…

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Q: 1. Ella thinks that if a function is positive over an interval, then its derivative is also…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Given,           ℒ-11s2+1s2+25

Q: xcsc (y/x) -y]dx + xdy=0 Prove that it is a Homogenous DE using homegeneity test (degree n) and…

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Q: What is the gradient of f(x, y) = x² - y4 at the point (5, 2)? O 5i + 16j O -15i-16j O -6i + 13j O…

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Q: Evaluate 09 9121IN N OC 2 01 2 1 2 I -1²-2 dydx.

A: Given query is to find the value of the integral.

Q: Evaluate (0₂2). [(x² + y² ]ds along the path C, defined as counterclockwise along the circle x² + y²…

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Q: Find the G.S. about xo = 0 for the following DE's 2. (1 + x²)y" + 10xy' + 20y = 0

A: answer is in next step. please give a like !!

Q: Solve the initial value problem. ds dt I cost- sint, s = 3 2

A: To solve the initial value problem.

Q: = Let f be a function defined for t≥ 0. Then the integral L{f(t)} . - fotº e- 0 provided that the…

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Q: 20 29t2 +42t represents the position function for a particle moving The function s(t) = along a line…

A: The given function is: s(t)=203t3-29t2+42t  where t∈0, 6 v(t)=d(s(t))dt=d203t3-29t2+42tdt=20t2…

Q: Question 9 of 20 View Policies Show Attempt History Your Answer Correct Answer Correct. Solve the…

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Q: Eliminate A and B. y=Ae2x+Bxe2x Oy -4y2y=0 Oy +4y +4y=0 Oy²-2y-4y=0 |y-4y +4y=0

A: Given a solution of differential equation as y=Ae2x+Bxe2x. We need to eliminate constants A and B,…

Q: If 6√√x + 15√y = 177, find y'(x) by implicit differentiation. y'(x) = Y I Find the exact value for…

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Q: Find the area enclosed by the polar r = 2 (1+sine) Curve

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Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

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Q: (x-2y) dx + (2x+y) dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n) and…

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Q: Evaluate the following limits. Show complete work x² - 4 X-2 X-2 a) lim b) lim (√x²+1-x) X→∞

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Q: Answer true or false. The function f(t) = (et) 10 is of exponential order. O True O False

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Q: Use substitution method to evaluate the definite integral fore dx

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Q: D) lim f(x)=| 23 E) lim → 8 f(x) = F) lim f(x)= z 2

A: D) we know that, limx→3f(x)=limx→3+f(x)=limx→3-f(x)But limx→3+f(x)=2limx→3-f(x)=-1Since…

Q: Let f(x) f'(x) = 3 sin r 2 + cos x Find f'(x).

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Q: Find x² - y²¹ lim (x,y) →(a,a) x² - y² O 2a O 2a² a² 00 DO

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Q: For the function f(x)=x²-5, write Newton's formula as n+1 = F(x) solving f(x) = 0. Type in x_n for n…

A: The given function is: fx=-x2-5 And the given Newton's formula is: xn+1=Fxn=xn-fxnf'xn   As we know…

Q: Question Find the linear approximation L(x) of the function f(x) = cos(x) at a = - 품. (Enter an…

A: We can find the linear approximation as below.