Ex/ show that f(x) = x+7x + 4 x + 1 has an inverse. %3D

Q: Write the f(x) = |3x − 1| in its piecewise-defined form.

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Q: 1 + 10/x| dx 3x3

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Q: In constructing an open rectangular box from 588 ft of material, what dimensions will result in a bo...

A: Given problem:- In constructing an open rectangular box from 588 ft² of material, what dimensions wi...

Q: Select all that apply. Solve for x, 0° g x< 360° sin 2x + 2 sinx cosx = 0 270 360 90 180

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Q: Question 1: Find the limits of the functions below a) lim,-3 2x3 sin x b) lim,

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Q: S. xdx (x²+2)3 A 2(x+1) 4(x²+1)2 B +C 2(x+2) 2(x²+2) 2 +C 4(x²+2) 2(x²+2) ? D 2(x+2) 2(x+2)?

A: Substitute, x2 + 2 = t.  

Q: (x² + 1)y' + 2.xy + 2x = 0

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Q: 1 – x2 + V1 – x2 In|(sqrt(1-x^2))-1|+c -In|(sqrt(1-x^2 ))+1|+c -In|(sqrt(1-x^2))-1|+c In|(sqrt(1-x^2...

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Q: Find the limits of the functions below a) limx-3 x* sin x b) lim,

A: We can find the limit of both the question as below.

Q: - 3x 2 + (コメオリ)』 = e Jス

A: Given: - The differential equation is, xdydx+(3x+1)y=e-3x To solve: - The solution of the given equa...

Q: Modeling a plane for takeoff. Using differential get the takeoff speed after 1 min. • (Airplane take...

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Q: (ii) L„(sin x) dx # 0 .

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Q: Determine whether the statement is true or false. If the statement is false, make the necessary chan...

A: Given: The inequality x - 4 &gt; 0 is equivalent to x &lt; 4. Now, x - 4 &gt; 0 x &gt; 4 So, The ine...

Q: Given: sin A = ! and cos x = - ; evaluate the following expression. %3D (8: Quadrant I, x : Quadrant...

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Q: Expand the function in a power series E a„x" with center c = 0. Find a,x". 7+6x n=0 (Express numbers...

A: Radius of convergence of the power series ∑n=0∞anxn is given by, R=limn→∞anan+1 The series ∑n=0∞1np ...

Q: п+1 а) Σ п+1 (-1)"*1 п-1 00 п (-1)" b) E 3" n=1 п 00 п (-1)"(5n–1) Σ 4n+1 n=1

A: In this question we have to determine whether the series is converges or diverges.

Q: Use integration by parts to show that for n > 2: / sin" x dx: 1 sin- x cos x + /sin-2 x dx.

A: To evaluate: ∫sinnx dx

Q: 6, Solve the IVP 3w" -u'+ 2u0. u(0) = 2, u'(0)-0

A: The given equation is; 3u"-u'+2u=0, u(0)=2,u'(0)=0

Q: dx 4. S x²Vx2-9

A: 4). Given: I=∫dxx2x2-9   ....(1)   As we know from the trigonometric identities; 1). cosx=1secx 2). ...

Q: 7. Which of the following is the potential function for F = (2ху + 1,х2 + 2yz, y? — 2)? а. Ф(х, у, 2...

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Q: sin³ydy |1+ cosy The is equal to 1 A.cosy +, cos²y+C 1 B. –cosy +, cos²y + C 1 C.-cosy -, cos²y + C ...

A: ∫ sin3(y)dy/(1+cos(y)) here put the value sin2(y) = 1-cos2(y)           = (1+cosy)(1-cosy) put this ...

Q: Find an equation of the line that is tangent to f(x) = x and parallel to the line y = 3x + 1 (Hint: ...

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Q: 1. Given y = log3 9. The value of y= %3D 2. If log(r + 2) = 4, then the value of r is %3D 1 3. If lo...

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Q: 5л? + 3х — 14 (а) f(*) %3D 5х — 4 6x² + 4/x (b) f(x) = %3D

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Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and find the nth Maclaurin polynomial...

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Q: 2. S dx 4-x2

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Q: For the given function f(x), determine the equation of the tangent line at the point P(1,1) f(x) = v...

A: Equation of tangent line

Q: 1 dx x /1 – (In x)² 1

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Q: PART I. Solve for x in each proportion. jewane 1uoy nislox3 inemetete yhslimie e shw x-5 3. x+3 15 2...

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Q: _8. If y = (2x + 7)², then what is ? dx а. dx dy 2(2x + 7) C. dx dy = 2 %3D dy dy b. dx = 4x d. = 8x...

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Q: A box with a top is constructed from a piece of 200-cm by 400 out and the flaps are folded to make a...

A: Given: - A box with a top is constructed from a piece of 200 cm by 400 cm cardboard. The shaded regi...

Q: 3 Consider the following function f(x,y) = +y° + 2xy - 6x- 3y + 4 3 3 3, 2 The critical points are A...

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Q: 7. Fill in the boxes below to create an equation equivalent to the equation x = 40. %3D log

A: 7. The equation is given by x3 = 40                         ..........1 To evaluate: An equation equ...

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to ...

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Q: lim -Vx + +sin(x)cos(x) 1+In (x)

A: Topic:- limits

Q: Use sigma notation to write the Taylor series about x = 8 for the function. 1 x + 5 k = OW

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Q: c) f(x) = V3sinx d) f(x) = x³tan(5x)

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Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d. f'(x...

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Q: 7. Cos? 3" cos n n=1

A: ∑n=1+∞cos2n3nBy comparison testcos2n3n≤13nSince ∑n=1+∞13nconverges by geometric test 

Q: x²-1 dx 1. S

A: Given: I=∫x2-1xdx   ...1   We know that the trigonometric identities; (1). The Pythagorean identitie...

Q: integrals and the limit definition per integral in your solution

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Q: 10. The following is a power series except for 00 00 (x – 1)" 00 (2х + 5)3п b. 2n Σ а. (2 — 5х)" nn ...

A: Power series is a series of the form ∑n=0∞ cn(x-a)n

Q: 3 x° +5 3, 2 X +x - X dx -

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Q: 2 1 2 A = = | 3 -2 4 -3 -5]

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Q: The temperature is T degrees at any point (x, y, z) in three-dimensional space and T(x,y, z) = 1/(x²...

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Q: The polynomial function f(x) is graphed below. Fill in the form below regarding the features of this...

A: Graph

Q: 19. Consider the parametrization of the unit circle given by c(t) = (cos t, sin t). (a) Verify that ...

A: We have to verify that c is parametrized by arc length and show that the curvature k of c is constan...

Q: Given: sing = and cos x = -; evaluate the following expression. (A: Quadrant I, x : Quadrant II.) si...

A: Multiple angles

Q: 1.(Easy) For the following differential equations, state the independent and dependent variables, th...

A: The objective of the question is determine the independent , dependent variables , order , degree an...

Q: what is cos(tan^−1(−1/2))

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