1. Let x₁0 for all ne N. (a) If xn0, prove that √x -0. (b) If xn →x, prove that √√√√x.

Q: At what point on the y-axis will the normal line at x = 1 of the function f(x)=√x intersect?

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Q: Find the Maximum value of the function f(x,y)=x^2−y^2−2y on the curve x^2+y^2=4.

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Q: dentify a technique of integration for evaluating the following integrals. If necessary, explain how…

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Q: 28. (2A + B²)4

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Q: 81.2² 18 3x-2 = For the rational function h(x) a. Find any intercepts of the function. State them as…

A: to find the y-intercepts, take x=0

Q: 1 2 ső ső (x + y) dydx 0 O none is correct O-3 02 0 3

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Q: 3. For Z= xtanxy,evaluate Zyy

A: The given function Z=x tanxy We have to find Zyy.

Q: Which of the following is the correct form of the partial fraction decomposition of OA.1 + B. 1 + L…

A: The objective is to find the correct form of partial fraction decomposition.

Q: 2x²-5x-10 (x+2)(x² −4) dx

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Q: 5. | tan’xsec*xdx

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Q: Tlake Home part of lest 1. Find the critical values. for f(x) = x² + 4x³+4x²

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Q: Let f(x,y)=sin(4x+8y) and P=(π/4,1/4π). Find the maximum rate of change of the fucntion f at the…

A: Given data ÷ fx,y=sin4x+8y   Now we need the maximum rate of change of the function. So,we need to…

Q: 3. On what intervals is h(x) = x² - 10 arctan(x²) increasing and on what intervals is it decreasing?

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Q: πT sin(x) S. "So" so 0 0 (1 + cos x) dydx 02 01 O none is correct Οπ

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Q: Solve the inequality. State the solution in interval notation: x ≤ < 1 - 2x x-2

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Q: Solve each of the following: (x − y − 2)dx + (3x + y - 10)dx = 0

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Q: Consider the following integral. Sketch its region of integration in the xy-plane. 0 LL 9-x² 6xy dy…

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Q: Find the rate of change of the area of a circle with respects to its diameter when the radius is 6/2…

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Q: By using the definition of the derivative, one can sin(x) - 1 x-x/2 2x - R Identify the correct…

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Q: 8. Let y find = dy dx 4x√x² +8 (x +9)2/3* at x = -1. Use logarithmic differentiation to

A: The given data is: y=4xx2+8x+923  Use logarithmic differentiation to find dydx at x=-1

Q: Find an equation for the tangent plane to the surface 6 z + 2 = xy cos(z) at the point (2, 1, 0).…

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Q: M3.2. d. A cadet engineer determines that when x hundreds of units of a particular commodity are…

A: We need to find out the instantaneous rate of change of P(x).

Q: Si 0 dx √√√x+1+1 7

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Q: e think of In(-3x + 7) as In(u), then u is a differentiable function of x and u = tionally, if we…

A: Topic:- application of derivatives

Q: 9. A Rectangular box w/an open top is to be made from a square piece of cardboard that is Binche's…

A: This question can be solved using the concept of maxima and minima.

Q: x + 3y s 18 2x + yΣ 14 x Σ Ο Υ Σ Ο

A: See this solution in below.

Q: Which of the following is not equal to logu? log, e 74 In(a) 74 1. 11. u.In a Il only III only OII…

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Q: The volume of a box is 10x3 + 27x2 + 2x - 24 with the length 5x - 4 and the width 2x + 3. Find the…

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Q: 6 5 4 3 2 -6 -5 -4 -3 -2 -1 lim h→0 -2 -3 -4 -5 2 3 4 y = g(x) is graphed above. Estimate the…

A: Given query is to find the value of the expression.

Q: Hello,  Could I please get help with this discrete maths question.  I'VE ATTACHED A PICTURE OF THE…

A: Your solution is correct.

Q: A frustum shaped bucket is shown as in the reference image. The top radius is 2 ft, the bottom…

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Q: Consider the ellipse foci? (x-5)² 256 + (y-7)² = 1. From any point on the ellipse, what is the sum…

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Q: Consider f(x) = 5x + 4 and g(x) = x² + 4x − 21. • You must combine all like terms before you submit…

A: Since, you have posted multiple questions, as per guidelines we"ll solve only first three parts. If…

Q: The volume V of a growing spherical cell is V= r³, where the radius r is measured in micrometers (1…

A: We have given V=43πr3, where r is the radius and V is the volume.  a) find the average rate of…

Q: A rectangular poster is to contain 162 square centimeters of print. The margins at the top and…

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Q: given costheta=5/13 with theta in QIV, what is the value of 2theta?

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Q: 1+tan^2x/sec^2x-sinxtanx/secx-cos^2x

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Q: Find the absolute maximum and absolute minimum values of the function f(t) = √t · (3 – t) on the…

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Q: Suppose that the plane tangent to the surface z=f(x, y) at (−1, 4, 5) has equation z+5x+1y=4…

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Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

A: Given query is to find the derivative of the function.

Q: xis that the terminal position of the angle resides in and state the value of the reference angle.…

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Q: 2x²-5x-10 (x+2)(x² −4) dx

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Q: A series circuit has a resistance R = 10 Ohms and inductance L = 2. The battery gives a constant…

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Q: Let Find the values of y = f(x) = 10x³ + 3x - 3. Y₁ = f¯¹(x)|x=83, Y2 = f¯¹(x)|x=-899 Y3 = f¯¹…

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Q: Find the indefinite integral using the substitution x = 5 tan(0). (Use C for the constant of…

A: Topic- Indefinite integral We are given,∫x525+x2dxx=5tan(θ)

Q: What change of variables is suggested by an integral containing √x²-324? Choose the correct answer…

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Q: Evaluate the double integral x cos y dA, where D is D bounded by y = 0, y = x², and ï = = 5.

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Q: ✓5. 4y³(x² +4) dx + 4xy¹ = (x² +4)² dx

A: Given differential equation:- 4y3x2+4dydx+4xy4=x2+42

Q: Concept check: Evaluate the following integrals and use the appropriate transformations when needed.…

A: Given integral:- ∫cot4t2dt

Q: Without using Synthetic Division, divide : (9x3 - x + 2) ÷ (3x - 1)

A: Given query is to perform synthetic division.