Find the absolute extrema of f(x) = x − 2 tan^−1 x on [−1,√3], and identify the values of x at which they occur.

Q: Use the properties of infinite series and the fact that Σ 1 1. 1 and 4 5" n = 1 6' n = 1 5 to find…

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: x² + x +2 Evaluate x2 – 1 (x– 1)2 - In- - +C x+1 x+1 In- (x- 1)2 +C X+1 x+ In- (x – 1)2 (x – 1)? +C…

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Q: Evaluate the indefinite integral. sin (r)cos(r)da + C

A: Explained below

Q: 2 - V2r + 10 a. lim 1-3 r2 + x – 6

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the first partial derivatives of the function. f(x, у) = 3x + 5y + 4 fy fy

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Q: dx Using Trigonometric Substitution J- , find f(0) = (x² + x + 1)7 O 3 sec? e 4 3 sec e 4 4 3 sec e…

A: The given integral,     ∫dxx2+x+132

Q: |v|dt. Then find the Find the arc length parameter along the curve from the point where t= 0 by…

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Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: Given: Now, fxx=∂2∂ x2x5+x2y2+y5+x+y    =∂ ∂ x5x4+2xy2+1    =20x3+2y2 fyy=∂2∂ y2x5+x2y2+y5+x+y…

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: As a group, discuss why there are no terms of the form x*, xy, or xy in the expansion of (x+ y)'.…

A: (1) In the expansion of (x+y)3, each term has the power 3 ,that' why x4,x2y2,xy  do not exist

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Vx² + 4x – 5 ,2 using Trigonometric Substitution find x Consider X+2 O -2 +3 sec 0 O3 sec e O -2+…

A: Here, the given integral is: ∫14x2+4x-5x+2dx=∫14x2+4x+4-9x+2dx=∫14(x+2)2-9x+2dx

Q: [2x+11 3 1 dx . evaluate Consider 3 1 dx x+3 dx = x2 + x- 6 x- 2 | x+3 X- 2 x+3 x- 2 In +C x+3 In…

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Q: C. ta the sum or the values of a and h such that f(x) - 2ax2 1 hr + 3 has a relative extremum at the…

A: 7.   The function f(x)=2ax2+bx+3 has a relative extremum at the point -1,2

Q: Consider the following function. f(x) = x – log, x (a) Find the critical numbers of f. (Enter your…

A: The given function is: f(x)=x-log4x       =x-ln xln 4

Q: dx Using Trigonometric Substitution find f(e) - 3 (x² + x + 1)7 3 sec e 4 4 3 sec? e O 3 sec? e 4 4…

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Q: 2n+1 5. Σ 'n°(n+1)² n=1

A: let  bn=1n3∑n=1∞1n3    is convergent   by p series  Recall ∑n=1∞1nP    is convergent  iff p>1

Q: | 2x+11 dx = Consider 1 dx evaluate 3. x² + x - 6 dx- X+3 X- 2 X+3 X-2 x-2 In + C X+3 |(x-2)3 In + C…

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Q: a) y=x² and y=2x+3 aJCurve accurately drown with important points lobeled b Strip is present,…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 4x3 + 4x? – 2x + 4 dx - (x² + 1)?

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Q: In how many ways can the digits in the number 8,400,000 be arranged? ways (Type a whole number.)

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Q: Find the area between the curve and the x-axis over the indicated interval. 7 y =; [1, 6] ... The…

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Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

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Q: 1. Evaluate the following limits. 2 - V2x + 10 a. lim 1-3 x2 + x – 6 4x – 7 1 lim с. -1- (3r2 – 2r…

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Q: dy Do not simplify your answers. dx 3. Solve for sec(3r? + In 2) evz+2 +9 (5x-1 – 3")* e3z Vcot() C.…

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Q: Find the indicated derivative in each using three-step rule. 1) f(x) = x² – 4x +3; f'(x)

A: Solution: As per our guidelines, we are supposed to answer only? One question ( if there are…

Q: dx consider Using trigonometric substitution, find u ar (x²+x+1)½ (A) u=x+1, a=- (B u=x+1, a=1 C)…

A: Topic:- application of integration

Q: What are the polar coordinates of the point P shown below? 2 3 4

A: This question is related to coordinate systems, we will solve it using given information.

Q: The function s(t) describes the motion of a particle along a line. s(t) = 12t – t2 (a) Find the…

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Q: Rewrite the expansions in terms of exponential and simplify the results as much as you can. cosh 5x…

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Q: (b) 1 When is the velociy of the particle positive? [0,1) U (3,4] When is it negative? (1,3) When is…

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Q: USING A- V2P de, FIND THE AREA OF ONE PETAL OF THE ROSE DEFINED BY THE EQUATION 3cin(2B)

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Q: Find the first partial derivatives of 2х — 4у - f(x, y) = at the point (x, y) = (2,2). 2х + 4y af…

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Q: Evaluate the definite integral. V4x + 3dx 0.

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Q: dx Using Trigonometric Substitution - f(e) - find (x² + x + 1) 2 4 3 sec e O 3 sec? e 4 4 3 sec? e O…

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Q: Calculate R4 for f(x) = (x-1)^2 on interval [2.4]

A: the given function f(x)=x-12 on the interval 2,4

Q: dx Using Trigonometric Substitution J- 3 sin e+C express the answer in terms of x. (x² + x + 1) 2 4x…

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Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. x + y 12xy -…

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Q: Using Integration By Parts, (2x2 e -Svau dx = uv- Find u v- Sv du- 1 6 x2 e - f12 x e3" ax Soxe s".…

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Q: Using Integration By Parts, Vx In 2x dx =uv- -Svdu Jv du Find UV- du O 2 늘 xVX In 2x-| Vx dx Xx In…

A: A detailed solution is given below

Q: s-8 3. (s-3)(s²+2s+17)

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Q: Find the area bounded by y = x+ 4 and y = x2 - 2. Answer:

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Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: Using Integration By Parts, Vx In 2x dx = u v - v du Find u v- ſv du O 3 xVX In 2x-|응Vx dx 2 xVx In…

A: We can solve this as follows:

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(6 + cos t) and 0= 5+ e where…

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Q: x² + x – 2 (3x – 1)(x² + 1)

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Q: Using Integration By Parts, x Arcsec 3x dx = u v - Jv du - iv- Svau. Jv du. Find uv- o Arcsec 3x -…

A: Given: ∫x Arcsec3xdx=uv-∫vdu   ......(1)   As we know that; The chain rule; fgx'=f'gx·g'x The Power…

Q: Write a in the form a = a- T+ anN at the given value of t without finding T and N. r(t) = (t + 5)i +…

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Q: Integrate: I+2dx + C

A: To solvethe following integral part