3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx S V1 + sin²x 6-

Q: If r(t) = (3t, 2t², 4t³), find r'(t), T(1), r"(t), and r'(t) x r"(t). r' (t) = T(1) = r"(t) = r'(t)…

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Q: Express the function n, lim n→+∞ 4k² in closed for and then find the limit. n³

A: We will first write this function in closed form then we will calculate the limit of the function.

Q: EXAMPLE 1(DISK METHOD) Find the volume of the solid generated by revolving about the x-axis,the…

A: Given problem:- EXAMPLE 1(DISK METHOD)   Find the volume of the solid generated by revolving about…

Q: (D² - 6D+9)y = 0

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Q: erivative 263.7 0.5cos0+ 0.3515.sim

A: Derivative

Q: 62-24 x²+2x-8 5. Analyze the function from its equation y determine the non-permissible value(s) the…

A: The non-permissible value of a rational functions are obtained by equating the denominator to zero.

Q: cost, y = sint, at the point where t 0 ≤t≤ 2π -O?! =

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Q: A pole that is 5625 feet long is leaning against a building. The bottom of the pole is moving away…

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Q: 11. S x + 4 x² + 5x - 6 dx

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Q: Shaw that is the function defined by xy f(x, y) = √x² + y² if O differentiable at not derivatives.…

A: Here in this question, we need to prove that the given function is not differentiable at the origin…

Q: =iven √x³√4-x² dx. If we letz= √√4-x², which of the following integrals is correct using…

A: We have to substitute z=√(4-x^2)

Q: Example 99 Consider the set M = {(x, y) = R²: x,y #0}. Find M. Solution:

A: The orthogonal complement are subspace

Q: Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. lim f(x)g(x) lim (2f(x) + 3g(x)) lim…

A: Given limx→-4f(x) = 3 and g(x) = 1.

Q: Let the vector v have an initial point at (−5, −4) and a terminal point at (−3, 1). Determine the…

A: We have to find component vector

Q: 2log, x-log, y+log, z

A: Follow the procedure given below.

Q: Solve the problem. The velocity of water ft/s at the point of discharge is given by v- 12.80/P,…

A: Given; v=12.8√p, pressure=20.00 lb/in^2

Q: P3: Calculate the volume of solid of revolution when the region bounded by y = sin 2x and x²-y-2 = 0…

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Q: wait so which option is the correct answer?

A: Solution:

Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: We need to choose correct option.

Q: 50° E 30° D In the figure above, line segment AC is tangent to the circle with center O at point B.…

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Q: 1. f(3x + 1)¹5 dx 2. f(8x³ + 2x² - 1)7 (6x² + x) dx x-2 3. f dx √50-5x3

A: LetI=∫(3x+1)15dx put  u=3x+1differentiate du=3dxdu3=dxThereforeI=∫u15du3Take constant…

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: y = x² and x² = y

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Q: find differential equation of the following equation 1) y' = y-x y+x

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

Q: b) Calculate (i) the following integrals x² (3x³ + 2)²dx

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Q: Find the directional derivative Duf (2,0) where, f(x, y) = xexy + y and u is the unit vector in the…

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Q: Solve using method of undetermined coefficients: 2y" + 3y - 2y = 14x² - 4x - 11, y(0) = 0, y'(0) =…

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Q: Suppose 8 3n f(x) = n! (x - 7) n n=0 7 To determine So f(x) dx to within 0.0001, it will be…

A: We have to find the value of integral.

Q: The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of…

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Q: A spherical water tank 1 ft in radius, has a spout of length 1 ft at the top of the tank, is full of…

A: Given problem:- A spherical water tank 1 ft in radius, has a spout of length 1 ft at the top of the…

Q: Evaluate the double integral over the given region R. xy SS dA x² + 1 R xy SS dA= x² + 1 R (Type an…

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Q: 27) 5 1 dx √x²- A) in (x+2+25+C In 5+X In +C 10 5-x nt B) +C X+5 D) (x+12-25374c In +C

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Q: Evaluate the difference quotient f(a+h)-f(a) for the function f(x) = x² + 4x - 5. h 2a +h+4 h+4 2a +…

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Q: π.χ. Evaluate the integral 8x sin y dy dx. 00 The value is. (Type an exact answer, using as needed.)

A: The given integral,    ∫0π∫0x8x siny dy dx

Q: Find the angle of intersection between the equations f(x) = 3x and g(x) = 4 - x 2 in the first…

A: Given f(x)=3x, g(x)=4-x2.

Q: 21. Jo 0 dx (x + 1)(x² + 1)

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y ( ) = 0 O y =…

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Q: Question 13 d²2 Which of the following satisfies the differential equation dx² A. y = e³x B.y = e-3x…

A: We need to choose correct option.

Q: y = 2 sin (20+ 4π 3 ^

A: Given query is to find phase shift.

Q: Let f(x)=x3−3x2−9x+25. Use the derivative f′(x)=3x2−6x−9 to determine the following values for f on…

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Q: Use definition of derivative to find derivative of the function f(x)=3/x+2, at x=-1

A: Given f(x)=3x+2    at x=-1To find f'(x) at x=-1

Q: y 3. The region bounded by the curve y=sec x, the x axis, the axis and the line x=0.25pi is revolved…

A: The given curves are; y=secx, y=0 x-axis, x=0 y-axis, x=0.25π So, the bounded region is as shown…

Q: 1.) Use Green's Theorem to evaluate the triangle with vertices (0,0), (1,2), and (0,2). $4x² ydx +…

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Q: 1000 1+9e-t The number of minnows in a back yard pond is modelled by the equation P(t) = Where is…

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Q: 1. Given f(x)=x+5 and g(x)=x²+8x+15 Sketch the graph of y=- _f(x) g(x) Mark the asymptote(s),…

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Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

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Q: f (x) = 2x+7 if -5=Xcl 8 If X = 1 14X=3 if 11x-2 31 If x > 3 IS this continuous at X=1 ? formula…

A: Any function f(x) is continuous at x=a if  lim x -&gt; a f(x) = f(a) i.e. Functional value at that…

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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Q: Q) find differential equation of the following equation (1 + x²) dy + (y - tan-¹(x))dx = 0

A: On solving this we will get