3t² + t 3 t→→∞ t³ - 4t + 1 11. lim r - p³ r→∞ 2 - r² + 3r³ 13. lim

Q: 1. Convert the following vectors to Cartesian form. a. 13 m on a bearing of 165° b. 120 km/h 20°…

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Q: The population of a country will quadruple in 2 years. If its current population is 13000, what will…

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Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 2, ....)…

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Q: 3. 00 Find the radius of convergence for Σ (5x) k=1 (a) (c) 5 1|5 (b) 1 (d) 0

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Q: Q5.2 You have been. given the equation Find a particular following differential solution. for it…

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Q: Assume that the side of an equilateral triangle is measured with a percentage error of at most 1%.…

A: Assume that the side of an equilateral triangle is measured with a percentage error of at most 1%.…

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Q: Solve the differential equation. dy 9x²y² dx = for y # 0

A: Given query is to solve the differential equation.

Q: Find the value of 3 sin(2x) sin(x) dx.

A: Given query is to find the integral.

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A: Let's solve x,y and z value by using cramer's rule.

Q: The following table shows the average life expectancies in several countries. Assume that all…

A: The following table shows the average life expectancy in several countries. All the premiums you…

Q: 34. S₁ x sin x cos x dx

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Q: Find the radius of convergence of the power series, where k is a positive integer. Σ(n!)kxn (kn)! 0…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = f*…

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Q: 121.8÷0.6

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Q: Find the first five terms of the sequence of partial sums. (Round your answers to four decimal…

A: The given series, 12·3+23·4+34·5+45·6+56·7+.... We have to find the first five terms of the sequence…

Q: Suppose f is a one-to-one, differentiable function and its inverse function f-1 is also…

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Q: Let s(t) = = v(t) a(t): = - 9t² +t- 2 be a position function. Find the velocity and acceleration…

A: To determine the velocity and acceleration functions.

Q: (5) Determine if the alternating series converges Σ(-1)^n. 8 n=2

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Q: Find the maximum and minimum values of the function f(x, y) = e subject to x³ + y³ = 54 Please show…

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Q: Given the function below ✓-45x³ + 72 Find the equation of the tangent line to the graph of the…

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Q: Give the standard equation of the circle satisfying the given condition. a. Contains the point(-2,0)…

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Q: (3) Use the Comparison Test to determine if the series is convergent. ∞ sin n n² + 2 n=0

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Q: -5 -4 3 3 2 - (1. 4.). M² - (2, ²).M - (1) M-C = , M3 -4 2-4 -3 -2 -1 Given Matrices:M₁ = and…

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Q: Consider the following. e¹ - 4x = 3 (a) Find the exact solution of the exponential equation in terms…

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Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

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Q: n ²+1

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Q: -4-x² - y² 4 component. For the function f(x, y) (-3, -3) that has a positive find a unit tangent…

A: Let's find unit tangent vector.

Q: Differentiate y = cot ¹(t) + cot ¹(1/t). y = [

A: We know that: The Sum/Difference rule: f±g'=f'±g' The Chain rule: fgx'=f'gx·g'x Use the derivative;…

Q: 16. S x² + 2 x + 2 dx

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Q: By natural increase, a city, whose population is 40,000, will double in 50 years. There is a net…

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Q: Consider a population P=P(r) with constant relative birth and dealt rate a and b and constant…

A: Given dPdt=kP-m

Q: Given that f(x) = 2x+cos(x) is one-to-one, use the formula to find (f ¹)'(1). (f ¹)'(1) = 1…

A: Given that :  f(x) =2x + cos(x)  is one to one    To find : (f-1)1 using the formula (f-1)'(x)…

Q: Use Euler's method with step size 0.5 to compute the approximate y-values Y₁, V2, Y3 and Y4 of the…

A: Solution:

Q: tan(x)=2/3 and cos(x) is positive or tan(x)=2 *over* 3 and cos(x) is positive

A: Solution

Q: A piece of wire of length L is cut into two parts, one of which is bent into the shape of a square…

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Q: Find the extreme values of the function and where they occur. y=x²-3x² +7x-10 The maximum is 6 at x…

A: Given query is to find the extreme values of the function.

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

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Q: Write the sum using sigma notation: -1+2+5+ 8 + 11 +...+ 116= Σ Β, where B, n=1 A = B

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Q: 1. Find the derivatives of the following functions: a) f(x) = 2x³ + e²x b) f(x) = ln (2x - 1)5

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Q: Consider the following. 62 1 + ex (a) Find the exact solution of the exponential equation in terms…

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Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: Problem 1. 1 (a) 100 2²2² + +9 dx Explain why each of the following integrals is improper. 4 1 (b) ²…

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Q: P(250) = JO 1 dx 0

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Q: Assume that marginal revenue is given by: dI(x) / dx = 2,500 - x - 2x2 a) Determine the revenue…

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Q: Find the absolute maximum and minimum of f(x, y) = 2x + 4y within the domain x² + y² ≤ 1. Please…

A: Given function:- fx,y=2x+4y Let gx,y=x2+y2-1

Q: T (a) F(t)=(cost+tsint)i + (sint-t cost)j for 0≤t≤2

A: As per the guidelines I can solve only first question

Q: The matrices A, B and C are given by and D=AB - 2C. Give the value of d 2,3. a) O-12 b) O-13 c) O-11…

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Q: Determine whether the series converges or diverges by comparing it to a p-series. ∞ ln  1 +  18 n…

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Q: Use the Quotient Rule to compute: ਹੈ y dy y+5æ

A: By Quotient Rule ∂∂xuv=v∂u∂x-u∂v∂v2