Determine whether the series is convergent or divergent. If the series is convergent determine the value of the sum. 00 1 2- +3

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Q: - (lim 11100 ce 1500 = 0)

A: Given limit function :-  f(n) =1500/2n   To check given function is continuous or not

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A: Let's find.

Q: Find T(t) and N(t) at the given point. π r(t) = 4 cos(t)i + 4 sin(t)j + tk; t = 2 T (7) 2 ㅠ N(₁) = [

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Q: I want all the laws of trigonometric functions and the laws of their integration

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Q: а) 2х, -3х2 +5х3 -2Хм = 9 5X2 +X3 +3Х4 = 1 7Х3 - Ху = 3 2Х4 =8

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Q: Monique sells disposable protective face masks made of local textiles for P 12.00 each. Define a…

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Q: Solve the differential equation: * (D² + 1)y = tan x

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Q: Question 15 The cost, in dollars, to produce a designer dog leashes is C(z) - 8x + 9, and the…

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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: ergence or divergence of the given series or state that the Root Test is in 1 n=1 non x.)

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Q: the vector-valued function.

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Q: Differentiate: arcsin (# )+ 0 1 (E) None of these O x/y O y/x 00 + arccos (-) = 1

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Q: (-3,0) (0, -1) (-1,-2) y = h'(x) (0, -2) (3,0) c

A: Given problem:- Suppose that h(x) is continuous everywhere, with the graph of h'(x) given on the…

Q: What are the cylindrical coordinates of the point whose spherical coordinates are (3, 5, 1)? r = 0 =…

A: Given: spherical coordinates ρ,θ,φ, here ρ=3,θ=5φ=π6 To find : cylindrical coordinates r, θ, z

Q: .3 t +y3

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Q: A table of values of an increasing function fis shown. X 10 14 18 22 26 30 f(x) -11 -5 -2 1 5 Use…

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

A: Let, the first number x and second number y. Given that the sum of first number squared ( x2 )  and…

Q: IF F. dr. F(x, y) = 9xi + 6yj C: r(t) = ti + √4-t²j, -2 ≤ t ≤ 2 Evaluate

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

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e, y = 1…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. (If you need to use ∞…

A: The given series is (2n)! /n2 , n from 1 to infinity.

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use ∞o…

A: The detailed solution is given below Thank you

Q: Consider the series (4x)n n n=1 Find the interval of convergence of this power series by first using…

A: Given problem:-

Q: Find DO NOT SIMPLIFY YOUR ANSWERS. 1. log √2x² + y + 2x² + y) + tan(x™ — ñ³) = sin¯^¹²(x² − 1) + ½ /

A: To dydx.log32x23+y+tanxπ-πy=sin-1x2-1+π2

Q: x² 5x w Given that f(x) 3 a) find f'(x) b) find the equation of the tangent line x = 1. 1 12. Given…

A: Let's find.

Q: Evaluate the triple integral zdV where E is the solid bounded by the cylinder y² + z² = 64 and the…

A: Here, to evaluate: ∫∫∫Ez dV where E is the solid bounded by the cylinder y2+z2=64 and the planes…

Q: Prove the identity. COS X 1-sin x 1+ sin x COS X Note that each Statement must be based on a Rule…

A: Solution )  cos x / ( 1 - sin x ) Multiply cos x in numerator and denominator =cos x × cos x /  […

Q: 5. f(x) a=-2,2 2 √4-x2 -2 x 2

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Q: = ||r' (t) x r' (t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7 sin(9t)j + tk Use the formula…

A: find curvature

Q: 01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where…

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Q: (D² - 1)y 2 1+ex

A: In this question we have to find the solution of the differential equation.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t²j|| dt =

A: ||xi + yj || = √x^2. + y^2

Q: = The Taylor series for f(x) = √2x − x² at a : 1 is Σ Cn (x - 1)”. n=0 Find the first few…

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Q: Find the integral of the following equation integrate cos(x + pi/3) dx

A: Given problem:- Find the integral of the following equation integrate cos(x + pi/3) dx

Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +7 1 lim t +∞o (?, ?) 5t² + 6'5t,

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Q: Find the area between the loops of the limacon r = Area = 5(1 + 2 cos 0).

A: We have to find the area between the loops.

Q: d. Write the equations for any vertical asymptotes. e. What is the value of f"(x) on the interval -3…

A: We need to fill in the blanks.

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A: The given integral is x2/3 +8 limit from 1 to 2.

Q: ind r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). r(t) = 2t²i - 2tj + 5t³k (a) r'(t) (b) r"(t) (c)…

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Q: 1- Find the area under one arch of y = cos3 x

A: To find the area under the arch we will integrate the given function under the limits of the given…

Q: Finding an Indefinite Integral In Exercises 75-78, find the indefinite integral. 1 75. dx 7x-2

A: Here is the solution:

Q: Theorem (Two-Path Test). Let f be a function defined by z = =f(x, y). If f has different. limits as…

A: limx, y→0, 0x2yx2+y2