Use the given graph of f(x)=√x to find a number & such that if x-4<8 then √x-2<0.4 2.4 -√x 2 1.6 ? 4 24 352-0 2. ?

Q: a) yp (t) =) yp (t) = A cos (2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) Q21) One of the following…

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Q: 2. If F = (3x² - 3yz)i + (3y²-3xz)-(32²-3xy find div curl

A: Given problem:-

Q: Investigate if the integral is convergent or not. Justify your answer.

A: Given:     ∫1∞dx1-x   Substitute u=1-x→dudx=-1                dx=-du   =∫1∞-1udu

Q: A giant spherical-shaped snowball is melting. If the radius decreases at the rate of 0.5 in/min, now…

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Q: (a) Solve the following: 4x¹dx (b) Explain with the aid of a sketch how this value can be confirmed…

A: Follow the procedure given below.

Q: Determine two numbers whose sum is 36 and whose product is the largest possible. 20 and 16 15 and 21…

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Q: 1) e5ln x+4Lny-Ln z qua

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: ?What is order of the equation (y"+2y+3=0) Second order O First order O Zero order O Third order O

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Q: = f(x,y) = x² Determine whether the function z = (why or why not) +y + y² for for (x, y) = (0,0) (x,…

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Q: If real and imaginary part of an analytic function are constants. Show that the curves given by u…

A: Function f(z)=u(x,y)+iv(x,y) is said to be analytic in a region R if:-(i) ux,uy,vx,vy exist and(ii)…

Q: | 1) 2Ln(√x + 3) + 2Ln(√x − 1) = Ln(6x - 7) 2)3x+2 = 27

A: This question is related to solution of equations, we will solve it using given information.

Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: lim x→0 1 x + S x 6571- S Ans 50.

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Q: Let f(x) = 2x² -5x - 7. Expand and simplify: f(x +h)-f(x) h =

A: The answer is given below:

Q: Given = (1 + x -- k) dy da 13 What is the value of k such that y is perpendicular to the curve y =…

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Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

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Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: 1) e5Ln x+4Lny-Ln z 2) 2Ln√x+2Lne√ - 2Lne* QV² + 2²

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Q: Use - -1-1(x Let f(x) = 9x +7 In (x+1), x>-1. Find - dx (Simplify your answer.) x=0 to find the…

A: By using ddxf-1x=1f'f-1x to find the derivative of the inverse at the indicated point. Let fx=9x+7…

Q: S dy ² + 4y+20) ²

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Q: Six 2 CSC ² 2x - x cos 2x) dx

A: We know, ∫cosmx dx= sinmx/m  ∫sinmx dx= -cosmx/m  ∫cotmx dx = ln|sinmx|/m  ∫csc²mx dx= -cotmx/m…

Q: At which point/s is the absolute value function not differentiable? x = 0 The absolute value…

A: Above question is solved.

Q: CD is a parallelogram with vertices A(0, 2, -3), B(2, -1, 4) and C(-3, 1, 2). Find the angl een the…

A: Follow the procedure given below.

Q: The function f(x) 2x³ = local minimum and one local maximum. This function has a local minimum at x…

A: The given function:fx=2x3-45x2+300x+6.We need to find its local minimum and local maximum.

Q: Deriving the formula for volume generated by revolving the first- 8x and the line x = 2 about =…

A: Given problem:- Deriving the formula for volume generated by revolving the first quadrant area…

Q: 20 e dx x Inx

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Q: Find the critical values (if any) of the given functions. With solution please.

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Q: Find the derivative: y = x [ln(x) - 1] O ln(x) - 1 о O x ln(x) O In(x) O 1 + In(x)

A: Given y=x[lnx-1]To find dydx:

Q: (D4 - 1)y = 7x².

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Q: let A be a bounded. Sup A non. n-empty set in R show that is a limit point of A.

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

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Q: Rewrite the following quantities mo 1) e5ln x+4Lny-In z 2) 2Ln√x + 2Lne - 2Lne*

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Q: 3 + 2x² √3+2 x2 O 2x 3 - +C X + + 2x + C x3 23³3³ +0 x³ + 2x + C O dx =

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Q: √4x²(x³-5) dx = x³ (x¹2 - 25x² + 250x6 - 1250x³ +6250) + c O 16(x³ - 5)4 + c O(³-5)5+c O (2³-5) 5+ c

A: See the details solution in below

Q: Solve the linear system of equations. 2x+v+6=-1 5x+y-3=14 7x-5y+2= = 7

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Q: Exercises A write the 1st 4 terms 1 2. 1:4 운 은데linity 2. 을 , I 141

A: Given that the series is

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: We have to use the Euler method

Q: c) What is the loss the company incurs when it tries to maximize sales (that is, produce the maximum…

A: Find out the loss the company when it tries to maximize the sales.

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

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Q: (b) [x² x²9x8 – 12x4 + 4 dx 2

A: We need to solve integral.

Q: 2x² + 3x + 3 (x + 1)³ - dx

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Q: P3: Calculate the volume of solid of revolution when the region bounded by y = cos x and x² - y - 2…

A: We have to calculate the volume.

Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

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Q: If you apply the direct comparison test to assess convergence of arctan ²k, k¹.01 to which of these…

A: Given

Q: The Laplace transform of signal xi(t) is shown below. Determine the initial value x(0)

A: Above question is solved.

Q: Consider the following. [u-5(6 - u³ +4²0) du Simplify the integrand by distributing u¯5 to each…

A: We know that integration power rule is given as - Integration of xn is xn+1/n+1 +C ; here C is…

Q: (2x-1) dx 1 2x²³²-x²-27x +36

A: …

Q: Let f(x) be the function 5x² - 7x + 6. Then the quotient f(5+h)-f(5) h can be simplified to ah + b…

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Q: f(x) = = 250 x1.40

A: As we know that; The Power Law: ddxxn=nxn-1 And a·f'=a·f', where a is constant.   The given function…