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Q: Determine how many terms of the following convergent series must be summed to be sure that the…

A: Here, the given series is: ∑k=0∞5(-1)kk! Let, ak=5(-1)kk!; k≥1

Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.

A: We will find integral using  trigonometric substitution.

Q: Find a bound for the error in the approximation T20 to the given integral (but do not calculate…

A:

Q: When demonstrating that lim 2x + 5 = 7 with ε = 0.2, which of the following 8- x →1 values suffices?…

A: Use definition of limit of the function

Q: x² + y² =a²

A:

Q: Find the general solution of the differential equation. y(5) — 11y(4) + 29y"″ − 11y" + 28y' = 0.…

A: Let's solve given diffrential equation.

Q: (a) Show that the function f(x) = x² 2 n! n = 0 is a solution of the differential equation f'(x) =…

A: The Solution is given below

Q: Solve the initial value differential equation: (x² + 1) + 3xy = 3x where y(0) = 2

A: Given Differential equation,x2 + 1dydx + 3xy = 3xandy0 = 2

Q: Complete detailed solution. What is the derivative of 1 1(x) = (2+²+ -x)(-+1+√x²) x+1

A: To determine the derivative of fx=12x-2-x-1+x4x+1

Q: 1. Find the general solution of: du dx _ _ y + xy² + x³ x+x²y+y² dy

A:

Q: 1. Find the exact val a) sin 3π 2 b) cot (210°) c) sec (-765°)

A: topic:- trigonometry  note:- As per our guideline if more than one question posted than only first…

Q: Solve 8 sin (7x) = 7 for the four smallest positive solutions

A:

Q: Determine if the geometric series converges or diverges. If a series converges, find its sum. 2 1 1…

A: Given the series, 18+182+183+184+185+........

Q: ∞ A function is a probability density function if it satisfies the following definition: 1: f(t)dt =…

A:

Q: We are trying to prove the following limit. Suppose that we have found a value of such that e =…

A: Given: limx→7 (2x-7)=7

Q: The derivative of a function of f at æ is given by provided the limit exists. f(x+h)-f(x) = Use the…

A:

Q: x - 12 Find the area bounded by y = x²1x56 (Round the answer to four decimal places.) x = 5, x = 6,…

A:

Q: A woman is on a lake in a rowboat located 1 mi from the closest point P of a straight shoreline (see…

A:

Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: Find the unknown angles in triangle ABC for the following triangle if it exists. C=52° 30', b=25.4…

A:

Q: It has been determined that the cost of producing x units of a certain item is 10x + 363. The demanu…

A: To find the revenue function, while cost and demand function of the product is given

Q: Use the comparison theorem with f(x) = 1 √x [₂² to show that 1 X- is divergent.

A: Show that ∫2∞1x-1 is divergent.

Q: 3. Let S be the surface defined by the vector function (2e" sin v, 2e" cos v, u²+u), Find an…

A: We are given in our question a surface S defined by vector function R(u, v) = <2eusinv, 2eu cosv,…

Q: If sin(0) and is in quadrant I, find the following: 7 Give exact values. No decimals allowed! cos(0)…

A:

Q: The graph of y=f(x) is given. Solve the inequalities. Write the solution set in interval notation if…

A: To solve the given inequalities for the function f(x).

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" - 4y…

A:

Q: You throw a ball (from ground level) of mass 1 kilogram upward with a velocity of v= 35 m/s on Mars,…

A:

Q: Check convergence of En=1c cos 5 -¹ (²) - cos ¹ (²1) n+1

A: Use series convergence test

Q: Q1 (a) Show that y= Ae²* + Be ³*, where A and B are constants, is the general solution of the…

A:

Q: 2x²+5 1. Answer the questions below and then graph the rational function: f(x) = x²+x-2 a. Vertical…

A: To find out the vertical asymptote, vertical asymptotes and also make the graph.

Q: What is the sum of odd numbers from 1 to 501. 2. Find the sum of the first 50 even numbers.

A:

Q: Use logarithmic differentiation to find dy/dx. dx = y = x²16 x² + 16 Need Help? Read It X > 4 Watch…

A: Solve the following

Q: 16. Find the exact value of: π a) sin¹(tan(- =)) 3 √₂ 2 b) sin(cos-1(-

A:

Q: You are a corporate attorney who earns $300 for each hour you work. You want a vegan poutine. The…

A:

Q: Use the figure to find the exact value of the following trigonometric function. tan (20) tan (20) =…

A: We can find tan(2 theta) by multiple trigonometric formula.

Q: 1. a) Use appropriate math terminology, from the unit, to describe the transformations that would…

A:

Q: The area of the shaded rectangle in the figure is A = /h. The possible errors in the length and…

A:

Q: dx 2- sin x

A:

Q: Evaluate the integral: r+∞ 1 dv v²+2v-3

A: We will find the integral.

Q: Find y as a function of t if 9y" +12y + 29y = 0,

A: 9y''+12y'+29y=0which condition y(2)=8, y'(2)=9To Find: y(t)

Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

A:

Q: Give some examples atleast three where basic comparison test fails . Also investigate convergence of…

A: Given : we will given the three example where the basic camparison test fails.

Q: Write an equation for the polynomial graphed below

A:

Q: Find the total differential. w = eбy cos(4x) + z7 dw (No Response)

A: Explanation of the answer is as follows

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 ≤ 0 <…

A:

Q: 4. The region bounded by the curve y = x² + 1 and the line y = -x + 3 is revolved about the x-axis…

A: We have to find the volume of solid.

Q: 9. Prove: csc(x)-csc(x)cos² (x) = sin(x)

A: To prove: csc(x)-csc(x)cos2(x)=sin(x) Note that, sin2(x)+cos2(x)=1

Q: f(g(x)).

A: f(g(x)) = 25/x2  provided the answer in step2 with solution

Q: Let f(x) = 3x² + 2x − 10; a = 1. 1. Use the definition to find the derivative function f' 2. Find an…

A: The given function is: f(x)=3x2+2x-10

Q: 3 1 21 0 0 25110 3 7 2 2 -2 6 13 5 -4 10 10 30-4 01-10 2 0001-2 0 0 0 0 0 (a) Find the rank and…

A: