Σ E n=2 n·ln(n)

Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: (0 if –2…

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Q: xY = 5x+6y + 2 4. X'y %3D e

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Q: Differentiate y=x^lnx

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Q: Yes,  you did not say what a is and what b is. Their values

A: Apologies for the inconvenience.   To find a and b we set the equations equal to each other and…

Q: Sz IF A-(-2 4) 2 3-( (-24リ Cュ Prove! CA *B) *C = AK( B+C)

A: We want to show the above equation is true.

Q: Question 5 Determine the magnitude of the com

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Q: f(x, y) = R is the rectangle bounded by +1 -5<x<5 and 0<y<1.

A: Given function fx,y=1ex2+1Region R is bounded by -5≤x≤5 and 0≤y≤1.Surface area of over region R is…

Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

A: Given

Q: f k车9. if D < X< 1. if 1大メ$4. if X7 4, 3-X X-3 IS the Functibn 9(x) Continuous on |I4 ? Un (-∞ 8,0)?…

A: check contineous between [1,4] g(x) = 3 - x2 between 1 to 4 check for 1+ and 1- for 1- g(x) = 3…

Q: 10. * -1 x CSc

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Q: 37 11 Let z < 1 < and sin (1) = -. Use a double-angle formula to find sin (21). 12 (Give an exact…

A: We have to find the given trigonometric quantity.

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) %3D Vf(4, 2) =

A: If f is a function of x and y then gradient of f is given by ∇f=∂f∂xi^+∂f∂yj^So, ∇fa,b is given by…

Q: The dimensions ofa veclangubr vegion are varying with the bimeltsaccotdng 1-28 Cm/see and Wazt+6…

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Q: 10. dx 1+cos 3x In(1+cos 3x) + C %3D - 3 _11. S 2(cos x)(sin²x)dx 2 + C 3

A: As you mentioned  only 10 &amp; 11 solved

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

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Q: 1. у %3D х+/x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: In Problems 17-20, find the indicated values of f(x, y, z) = 2x - 3y2 + 5z - 1 19. f(6, -5, 0)

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Q: 5. Use L'Hospital's rule to compute the following limits (a) lim a In(x) (b) lim sin(z) (c) lim…

A: Here are the solutions: We will use L'Hospital rule and differentiate the numerator and denominator…

Q: 7. * In [In (In æ)]

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Q: n evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth…

A: Given query is to find the solution of the differential equation.

Q: The figure below shows the derivative F'.If F(0) = 15,give (x, y)-coordinates of all local maxima…

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Q: Given the region bounded by y=×^3 ,X = 2, and the x-axis (in Quadrant I) is rotated about the line y…

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Q: M3.4 Integration by Partial Fraction Decomposition 6x-7 dx 7.J (2x+1)(4x²+1)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Simplify (x) and find any vertical asymptotes. x²_ 4 f (x)= x+ 2

A: Vertical asymptote of the rational function f(x)=p(x)q(x)is given  q(x)=0

Q: Use a trigonometric identity to find cot ( - x) if tan (x) = 8. (Express numbers in exact form. Use…

A: Topic = Trigonometry

Q: QUESTION 12 Solve the problem. Suppose you wish to prove the statement that follows using…

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

Q: х3 — 4х? 8(7x – 4) (x + 2)* x(х + 8)(х — 2) | Given: f (x) : with f'(x) ,аnd f" (x) - %3D (x + 2)2…

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Q: Exercise To Try 5 Find the area under the curve y = 2x +1 and above the x-a interval (0, 3]

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: f(t) = -16t2 +385t +8 avg height from t = 5 to9.7 second f(9.7) =-16(9.7)2 +385(9.7) +8…

Q: 4. How many fixed points does the function T(x) = tan(x) have? %3D

A: for fixed point f(x) = x x = tan(x)

Q: dy dx Assume x and y are functions of t. Evaluate for 4xy -3x + 5y° = - 210, with the conditions dt…

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Q: Finding Vertical Asymptotes In Exercises 63–68, find any vertical asymptotes of the graph of the…

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Q: Find a formula for f'(x) and determine the slopef'(2) for the following function. f(x) el+8r' In(x+…

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Q: 18g(x) - f(x)]dx =] %3D 2 (Simplify your answer.)

A: This question is based on substitution of given integral.

Q: Find if dy y2+4 + In(x + 2) = xy3 dx 2vx+4 2yvx + 4 - 3xy² x + 2 Vx + 4 -3xy? 23Vx +4 1 x+2 2x+4…

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Q: Determine the interval(s) on which the function is continuous: 2r+ 7 212-3x-9 if x 1/2 Ox1/2 Ox1/2…

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Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x&gt;3To find : Find the values of a and b such…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Given: 2x+5y=-7; x-38=y2=z-714 Let, x-38=y2=z-714=t ⇒x=8t+3; y=2t; z=14t+7

Q: xD'(x) Find the demand function q = D(x), given the elasticity conditions. Recall that elasticity of…

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Q: Assume s is an angle with sin (s) = . t is an angle with cos (1) = and both angles are between 0 and…

A: We have to find the given trigonometric quantity.

Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: Find the area bounded by the curves y=8x-x2 and y=x2, and the line 4x-y=-12.

A: I have appended the formula used in the solution part.

Q: The dimensions of avectargubr region are varying with the bimeltsaccoding 1-2728 cmfsee and wa3t+6…

A: L= 2t2-8w= 3t+6Let A be the area of rectanglegiven : dAdt= 360 cm2/sec   A= L×wA=(…

Q: n3 - 2 1. Find Lt n+0 2n° + 3n - 4

A: Simplify the fraction and solve the limit.

Q: Find the distance between the skew lines i(t) = (3, 0, – 2)t + (7, 9, 0) and p(s) = (4, – 4, – 5)s +…

A: We have to find the distance between skew lines.

Q: 3 5 where x and Зл < y < 2n. Assume that sin (x) = sin (y) = - Calculate cos (x – y). (Give an exact…

A: Here, sin x=35; π2&lt;x&lt;π⇒cos x=-1-sin2x=-1-352=-1-925=-25-925=-1625=-45 And, sin y=-56;…

Q: Let z(x, y) = xy where x = r cos(20) & y = r sin(30). dx dy ду az & dr az Calculate by first finding…

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Q: Determine whether the lines are parallel or identical. x - 3 y + 8 z + 7 5 y – 1 _ z + 22 4 -3 x + 9…

A: The given two lines are                 x-34=y+8-3=z+75 and        x+9-8=y-16=z+22-10 We first find…

Q: A firm's marginal profit, P, as a function of its total cost, C, is given by the equation below. a)…

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Q: Determine whether the statement is true or false. Justify your answer. 5x +5 Ax +B Cx +D For the…

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