Using Sandwich Theorem 3n2 + 1 an = (-1)" n³ – 4 converges to 0 O converges to -1 O none of them O diverges O converges to 1

Q: first octant 2 4- x+y dy dx -

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Q: 324-y' y dx dy 18

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Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: Evaluate the triple integral. xy sin(yz) dV, where G is the rectangular box defined by the…

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Q: Find the area of the region inside the circle r = 30 sin 0 and outside the cardioid r = 10+ 10 sin…

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Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A: We have to find the surface area.

Q: Find the volume V of the described solid S. A right circular cone with height 3h and base radius 4r…

A: Solving the problem by finding the volume of the cone.

Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5, x=4, and…

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Q: Find the length of the curve, L. y? = 64 (r+ 5)* , 0 0

A: To evaluate the length of the given curve.

Q: Express the area of the given surface as an iterated double integral, and then find the surface…

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Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t att-0. x =…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is resolved…

A: Solution is done in step 2

Q: (b) A spring exerts a force of 4.2N when stretched 0.7m beyond its natural length. How far beyond…

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t+o 5t2 + 6't (?,?) - (

A: We have to find limit of given function

Q: Sketch the region enclosed by the curves and find its area. y = cos 4.x, y = 0, x 8' 4 NOTE: Enter…

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Q: 1009 1010 Suppose R= E (2k) = 2 + 4 +6+.+2018 and S= D (2k-1) =1+3+ 5+.. + 2019 What is the value of…

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Q: Use a double integral to find the volume of the region under the graph of f(x, y) = xy and above the…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: 2 2 3 Y= (4x3 - 4a3 ) 2

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

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Q: f(x, y) = x3 - y³, P(4, 3), v = (i+ j) %3D 2

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Q: Compute f(x)dx 2x if x 1 f(x)

A: To find out the integration.

Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: Given:          Curve y=2x2+10                     y=4x+16

Q: Evaluate JJ Xy dA, where R is the region in LA ... y = x? R 2 A) 13/7 B) 16/3 c) 18 D) 20

A: A detailed solution is given below

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -180 J-120

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Q: (8) Using Taylor's formula, e" log(1 + is approximately equal to (a) x – xy (b) х — ху + 2 (c) x +…

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Q: (1 point) Use the Divergence Theorem to calculate the flux of the vector fields F, = -Szi + 5xk and…

A: Find your answer below

Q: cos x csc3 x + C sin4 x 1.

A: To evaluate the given integral.

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) dx…

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Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

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

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = t - 8, s(0) = 4,…

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Q: dx 2 X + 4

A: Topic = Integration

Q: Find div F and curl F if F(x,y, z) = 4y®z³i – 7x°z*j – 3xy°k. div F=|0 curl F=

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Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: Use The Formula К(T) = ||R' (T) × R"(T)|| ||R'(T)|

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Q: 1. Find the equation of the tangent line to the curve x = e', y = et at t = 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find V· (V × F), if F(x, y, z) = 7e2*i+9xe³j – e=k. V · (V × F)

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Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Let's find.

Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

A: When a particle move on a circular path , the direction of velocity of the particle along the…

Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: Consider the following functions. f(x) = 4 sin x g(x) = 4 cos 2x Sketch the region bounded by the…

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

Q: Calculate the derivative of 2t – 1 > t + 2 r(t) =< 3t – 5, 2t2 + 5t + 7,

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Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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Q: intercept

A: Please refer to the image below