The density function of X is:  f(x) = c·x2 ·( 1 - x ).  Calculate the mode of X.

Q: State whether the following series is Convergent or Divergent. Σ (-1)" √n /n + 1 n=1 Absolutely…

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Q: Which of the following series converge? cos(mm) η n I. Σ 2 n+2 n=1 (A) None (B) II only (C) III…

A: 1.  series divergence test

Q: Consider the curve defined by the equation xy=21. Set up an integral to find the length of curve…

A: given  xy=21formula for length of curve L=∫x1x21+(dydx)2dx

Q: 5. Evaluate the following limits. 1 a. lim X-4+X-4 3-x² x→∞ 2x²+1 b. lim

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Q: Which ordered pair represents the coordinates of point B?

A: There are four points A,B,C,D. We have to find coordinates for point B.

Q: ja √√₁²-y² Va2-22 -√a²-y²-√√a²-x² - y² √√a²-x²-y² α ,2 2 ,2 (x²z+y²z+z³) dzdxdy

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Q: For a sequence {a} satisfying Σ4" an > 0 A B C D E F A) n=1 Σ4" an B) =1 diverges. Σ6" an Σ6" an…

A: Given that , an+1an→15

Q: УА 1 0 y=9 y=x3+ 1

A: For a rotation about y-axis, the solid will look like as below A circular disc of thickness dy of…

Q: Given the matrix equation: 1 [223] [] -2 4 -18 Which of the following represents the solution to…

A: The matrix equation is given by 13-24xy = -1-18 To determine: The solution of the equation.

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Q: ← Let f(x) = 2√x -x. a. Find all points on the graph of f at which the tangent line is horizontal. 1…

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Q: Question #4 - Find the derivatives of the following functions A) f(x) = LN(*²-7) 2x

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Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: We need to find the limit of the sequence limn→∞cos2n

Q: 3 Let f(u) = u³ and g(x) = u = 2x³ + 4. Find (f o g)'(1). (fog)'(1) = (Type an exact answer.)

A: Given query is to find indicated derivative.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: Given limit an = ( 1 + 7n )n

Q: Suppose the function g(x) has a domain of all real numbers except x = 8. The second derivative of…

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Q: te f(x) = x 2-12 X-4

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Q: 6x-7 (2x+1)(4x²+1) 4. S -dx In(4x² + 1) - 2 ln(2x + 1) -Tan-¹(2x)] + C

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Q: Which of the following differential equations is/are not separable? dy I. = dt X 1+t yt 11. y = 3xy…

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Q: Indicate the points at which the function shown in the graph above has a global maximum, a global…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: 10 1 1 1 [1 0 0 1

A: As per our guidelines we only solve one question and rest of the question will be reposted.…

Q: The part of the sphere x² + y² + z² = 4 that lies above the plane z = 1 (evaluate later as an…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 5. Determine the average rate of change in f(x) = √x + 11 with respect to x from x = 5 to x = 5 + h.

A: f(x)=x+11from x=5 to x=5+hfavg=f(b)-f(a)b-a

Q: In the summer, humidity interacts with the outdoor temperature, making a person feel hotter because…

A: Solving the following problem

Q: Determine the area of the region bounded by y = x³, y = -x³ + 1 and the y-axis

A: We first need to plot the area ÷ Shaded region is our area to be determined.

Q: For each of the questions below, indicate if the statement is true (T) or false (F). (a) A…

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Q: 1. Suppose for all n, an and bn are positive. If lim n-x Σan = 6 then Σαπ n=1 n=1 bn is also…

A: To solve the following problem

Q: -4x+3y=8 x-5y =-19 To solve the given system by substitution, the first step could be to solve the…

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Q: For the function f(x) = 4+ 12x²-x³, find the local extrema. Then, classify the local extrema using…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: The sequence have alternate negative and positive terms. This is possible only when we introduce…

Q: A quadrilateral has vertices A(−3, 1), B(1, 8), C(6, 7), and D(5, 2). Which kind of quadrilateral is…

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Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

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Q: Find an equation of the plane through the point p=(2,1,-4)  and perpendicular to the line x=2+3t,…

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Q: cutting

A: A fraction denotes part of a whole. For example: 23 denotes 2 parts out of total 3 parts.

Q: Solve the system of linear equations. 2x + 4z = -18 -4x - 2y 2z = 14 x+y=z=2 O No solution O(-2z-9,…

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Q: Find the limit of the sequence. {√3,√3√3, √3√3√3, ...}

A: 0⁰Pp⁰

Q: A farmer has 800 meters of wire fence with which to build two identical rectangular pens that share…

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Q: Find the interval of convergence of ∞ Σ n=0 (x-7)" n8 +2 (Use symbolic notation and fractions where…

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Q: f(x)dx = F(b) - F(a) and ſf(x)dx = P(x)+C. Consider the two expressions A) a and b are called the…

A: Given expression ∫abf( x )dx = F( b ) - F( a ) ∫f( x )dx = F( x ) + C

Q: The amount A of dollars accumulated after t years through an investment of Ao dollars at an interest…

A: Given query is to find doubling time at indicated rates.

Q: 4. Plot the points A = (1, -1), B = (4, 1), C = (2, 2) and D=(5, 4) and form the quadrilateral.…

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Q: Express the surface area of the surface obtained by rotating the graph of y = 5 sin (x) for not…

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Q: Separating the variables in the equation ye ΧΟ A. ydy = xe dx B. ydy = xe da C. None of these. The…

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Q: A fish population at a fish hatchery, y(t) (t in years), is modeled by the differential equation…

A: Note:- These are multiple sub parts and according to company we can do maximum 3 sub parts you can…

Q: K Solve the logarithmic equation. X= 1 - log 36 6 =X (Simplify your answer. Type an integer or a…

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Q: Consider the following. u =(4,-1,0) v = (-4, 7, 0) Find u x v. Determine if u x v is orthogonal to…

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Q: Calculate the derivative indicated. d²y dx² x=3 where y = 9. 1 x 3 +3x²

A: given: y=9x3+3x2

Q: Convert each exponential equation to the corresponding logarithmic equation.

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