lim,0+ ((sinx)tan

Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

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Q: 1- x, x 2 - Which of the following is TRUE? O The function is continuous everywhere. O The function…

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Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: A projectile fired downward from a height of 112 ft reaches the ground 2 seconds. What is the…

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Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: A rotating light is located 15 feet from a wall. The light completes one rotation every 2 seconds.…

A: Rate

Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: Find V · (V × F), if F(x, y, z) = 2e"²i+ 2xe"j – 9ev²k. V· (V × F) =

A: Given F(x,y,z)=2exzi→+2xeyj→-9eyzk→ To find, ∇.(∇×F)

Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: 5xdx 3. Find the integral (x-1)3 -5 5 а. 2(x-1)2 + C x-1 -5 b. 2(x-1)2 + C x-1 c. In (7DE) – in () +…

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Integral

Q: Solve the problem. Let D be the region bounded below by the cone z-x2+y2 and above by the sphere z-…

A: Given

Q: t cos t?dt can best be evaluated by: A None B Trigonometric Transformation Integration by Parts…

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Q: (x² + y2 + x)dx + xydy = 0 %3D

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy

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Q: d 10.(4* tan x) dx

A: Find the derivative

Q: Use Green's Theorem to evaluate the line integral. | y? dx + xy dy C: boundary of the region lying…

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Q: Q1: Find the length of a and b in the following triangle a 75 30

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Q: d Calculate ri(t) · r2(t)] and d [ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: dx 4. Find the integral 2-1)3 a. In (**1) b. In () - + C x-1 2x2-2 + C x-1. 2x2-2 c. - In -+ C 2x2-2…

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Q: Find div F and curl F if F(x, y, z) = 14y°z°i – 10x°z°j – 5xy°k. 35: 6.8 - div F= curl F=

A: We have to find div F and curl F.

Q: 2. lim

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Q: Evaluate T COs(T-a)-sin 글(ㅠ- z) - ㅠ lim T - x

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Q: x 1 What is lim f(x)? x→-1 O 3 O 4 O 2

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Q: If the function f(x) is continuous in the interval [-7.0] and f(-7) = 32 and f (0) = –1, then which…

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Q: 2.) f x²(2x³ + 1)5dx

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Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t< 7 L = e - e- - 0

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Q: Obtain the limits of the following functions: (2sinx-sin2x 1. lim x-sinx

A: To evaluate the limit of the function.

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 4tj – 6/ik) dt

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Q: 3. Evaluate the integral 7/4 1 + cos²0 do cos²0

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Q: Find the radius of convergence, R, of the series. xn + 1 3n! n = 2 R = Find the interval, I, of…

A: A detailed solution is given below.

Q: Evaluate the integral / (8x + 18y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: We have to find value of given Integral along given Curve.

Q: ind the arc length oI the parametric curve. 0 = 6 cos (t), y = 6 sin(t), z = 8t; 0 stST

A: Given: x=6cost, y=6sint, z=8t

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: f(g(x)) = (3x² f (g(x)) = (x)(x² +3)² (За* — 2х + 4)°

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Q: Which integral corresponds to the area of the shaded region between the curves y = |a² – 4| and y =…

A: To find the area of the shaded region.

Q: Find a Taylor Series for the function about x = 0. F(x) = In(3 + 4x) %3D

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Q: Find the indefinite integral. (Use c for the constant of integrat (4t3i + 4tj – 6vik) dt

A: we use the basic formula ∫xn dx =xn+1n+1+C    ; n≠-1

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: We have to find the values of vector valued functions.

Q: Q-What is the volume of the solid obtained by rotating the region bounded by the graphs of y = vx, y…

A: Volume of solid of revolution

Q: Q4: Find the corresponding Spherical polar coordinates of the Cartesian coordinates (6,2,5).

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

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Q: 1) Find and of the following equation then simplify whenever possible. dx dx² x = 2u* – u³ + u – 11…

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Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

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Q: pe of a trail at a distance of x miles from efinite integral of f(x) from x=3 to x=5

A: answer is in next step

Q: On what intervals is the function f(x) = continuous? x(x - 1)(x- 2) 1. (-00,0) 2. (0,1) 3. (1,2) 4.…

A: First draw the graph Uasing limits and the check the countinity of this function

Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

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Q: 7. S x4 sec (x5 - 9) dx 8. S tan 3 x dx

A: Question 7 and question 8 are solved.

Q: 13) Determine the lim X--9 + 169 く+9

A: Since the student has posted multiple questions and does not mention any specific question, so we…