Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) - 2 cos(r)- √2

Q: Convert the following point from cylindrical to rectangular coordinates: (x, y, z) = (5.5.-9) 5, 2

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Q: Find all the values of x such that the given series would converge. 8 8n (x²)(n+1) (n+8) n=1 The…

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Q: Write an equation of the tangent line to the curve f(x) = 3x/√x-4 at the point (5,15). Express the…

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Q: Using an appropriate substitution | tan³x sec7xdx is equal to

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Q: Derivatives of Transcendental Functions Directions: Find the derivatives of the following items.…

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Q: Differentiate the function and simplify the final answer. y = 2xsin x - x^2cosx

A: Given,y=2xsinx-x2cosx

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: 4 = Suppose sin 0 = and is in quadrant IV 5 Find the exact values of the other five trigonometric…

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Q: 3. Find 1. Lim f(x) 2. Lim f(x) 3. Lim f(x) 4. Lim f(x) n→∞0 n→ ∞ n→0+ n→0- x < 0 When f(x) = -&…

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Q: f(In x)2 dx O-r(Inz)² - zlnz+z+C -z(lnx)² + zlnz+ 2z+C O-r(Inz)² - zlnz+z O None of the choices…

A: Answer :- None of these choices

Q: cscxdx 5+ cos²x sin²x

A: solution:-∫csc25+cos2xsin2xdx,    {…

Q: Consider the function 2x+6 f(x)= x²+6 Find the critical point(s) off. (Give yourans wer in the form…

A: f(x) =(2x+6)/(x2+6)  Find:- Critical points  Local maximum and minimum at x= Interval function…

Q: Determine all solutions of the given equation. Express your answer(s) using radian measure. (Select…

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Q: Calculus optimisation problem Amount of fuel 'F' (in litres) required per hour to propell his…

A: Given, F(u) is the fuel in liters required per hour. u is the speed in kn/hr u(max)= 40 km/hr F(u)=…

Q: 5. Lim xsinx x-0+

A: Let A=limx-&gt;0+xsin x

Q: The graph of a rational function, f(x), has a point of discontinuity when x = 2 and an asymptote…

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Q: ₁√x³ √4-x² dx. if we let z = √√4-x², which of the following integrals is correct using rationalizing…

A: The given integral,        ∫x34-x2dx

Q: d dx tan x = sec² x

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Q: Solve the following equations by using Cramer's Rule 2x + 2y + z = 1 x-y + 6z = 21 3x - 2y-z = 4

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Q: Given the following matrix below, find matrix C such that A + 2B = C 2 -31 [3 -1 21 A= 5 0 2 & B= 4…

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Q: 1 to 21. Use the Cauchy-Riemann conditions to find out whether the functions in Problems 1.1 to 1.21…

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Q: Convert the following point from spherical to rectangular coordinates: 4π 11π (8,36 471, 117).

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Q: 18 The value of f (3), for the following function f (x)=√√2x-2 14 A C There is no real solution BC…

A: We have to find Function value

Q: Evaluate the integral directly by integration with respect to x and y. 7 x=(y/5)+1 5x-y S S dxdy…

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Q: Numerical Integration: 1 √x 1. 0 dx

A: We can find the solution of the definite integral as below.

Q: 8y^4+12y^3-2y divided by 2y^2+y

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Q: Sand is pouring out of a pipe and is forming a conical pile on the ground. The radius of the pile is…

A: Given:-radius of the pile  is increasing at a rate of 4 ft/daydrdt=4 ft/dayheight of the pile is…

Q: Prove that the vectors v= and w= are orthogonal.

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Q: 3 The absolute minimum value of f(x)=x³ on the closed interval [-1,8] is a) 0 b) -1 c) 1 2 d) -…

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Q: Find the average value of the function f(p, ,0) = p over the solid ball p ≤7. (Simplify your answer.…

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Q: The volume of a cylinder of height 12 inches and radius r inches is given by the formula V = 12². dV…

A: Given query is to find rate of change of volume.

Q: 5- prove that - for sin Ꮎ dᎾ cose Ꮎ dᎾ

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Q: lim₂+-1 f(x) = C 2

A: limit exist when

Q: Find where the curves intersect, draw a sketch of the region (label it completely), and compute the…

A: This question can be solved using area bounded by curves.

Q: Consider the following graph. 1 1 X

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Q: A company produces a special new type of TV. The company has fixed costs of $454,000, and it costs…

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Q: 1 S √4x²-9 Ocosh-¹+C -1 -1 Osin ¹+C Osinh¹+C O None of the choices Ocos ¹+C -1 dx

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Q: 5. Let f(x)=log, (x+1). a. Complete the table of values for the function f(x)=log, (x+1) (without a…

A: We are given f(x) = log3(x+1)  We have to find  Values of f(x) for following values of x without…

Q: In your own language, describe the pattern of the following sequences (The sequences are given as a…

A: We draw required connection between the pattern and formulas as below.

Q: √√√√3²-1 For the integral X What is the re-write of this integral? -dx, let z= x² - 1.

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Q: √√√x ²-1 d For the integral What is the re-write of this integral? Ⓒ / - A z² dz 2(z² + 1) B…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. 2. An In(n+1)…

A: 2.an=lnn+1-ln n

Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the…

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Q: [f(a)]² =

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Q: 7.Find of z = 2x³-5xy² 8²z xy

A: topic- partial differentiation

Q: A population of 800,000 microbes increases at the continuous rate of 4% per day. a. Carefully sketch…

A: Given: population of 800,000 microbes increases at the continuous rate of 4% per day. Find: sketch…

Q: (4x+5y=-3 5x+4y=3} x=-3 and y=3 x=3 and y=-3 .B x = -3 and y=-3.0 ( x=3 and y=3 DC Solve this system…

A: we have to find solution

Q: y = 3sin (40 +

A: Given query is to find the phase shift.

Q: Find [-2,3) n (-1,5) (3,5) .A (-4,-1) BO [-2,5) .CO (-1,3)

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Q: Describe the surface. x² + z² = 1 O sphere O ellipsoid O hyperboloid O circular cylinder O elliptic…

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