State the following.(a) The Test for Divergence(b) The Integral Test(c) The Comparison Test(d) The Limit Comparison Test(e) The Alternating Series Test(f) The Ratio Test(g) The Root Test

Q: Solve the equation sin 2x = √3 sin x on the interval [0, 2π). Use exact values where possible or giv...

A: We have to solve the equation: sin 2x=3 sin x in the interval x∈[0, 2π) We know the identity, sin 2x...

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A:

Q: Find the sequence of partial sums S1, S2, S3, S4, and S5.

A: Given: 1+12+14+16+18+110+.. To determine:  The sequence of partial sums S1, S2, S3, S4, and S5.

Q: Parallel, intersecting, or skew lines Determine whether the following pairs of lines are parallel, i...

A: r=3, 1, 0+t4, -6, 4R=0, 5, 4+s-2, 3, -2 The vector parallel to the line r is 4, -6, 4=-2·-2, 3, -2. ...

Q: Minimum of a Sixth-Degree Polynomial Find the minimum value of the function f(x) = 2 + 16x + 4x [Hin...

A: Given function is fx=2+16x3+4x6. Let t=x3 So, the function becomes: ft=2+16t+4t2=4t2+16t+2 This func...

Q: You place a frozen pie in an oven and bake it for an hour. Then you take the pie out and let it cool...

A: You place a frozen pie in an oven and bake it for an hour. Then you take the pie out and let it cool...

Q: Find the derivative of the function. y = (x2 − 6)3

A:

Q: Two or more equations that have the same solution set are called_________ equations.

A: Two or more equations that have the same solutions set are called equivalent equations. Equivalent e...

Q: Define what linear first-order equation forms?

A: Linear differential equation: a linear differential equation is a differential equation that is defi...

Q: Q27

A: a) Given data: The total height of the conical tank is H=12 m. The given surface diameter of the tan...

Q: Derivatives Find the derivative of the following functions

A: Given:y=4-xsinxProduct rule:ddxuv=uv'+vu'

Q: Determine whether the relation is a function. Give the domain and range for the relation : {(3, -2),...

A: we have to determine whether the relation is a function or not also we have to write there domain an...

Q: Mean Value Theorem for quadratic functions Consider thequadratic function ƒ(x) = Ax2 + Bx + C, where...

A: Given: fx=Ax2+Bx+C we know that given quadratic function is continuous on a,b and differentiable on ...

Q: * use the binomial seres to estimete (the first three ) 35 70 134 /1.5

A: 1) Given problems are, 70313031.52

Q: Differentiate. f(x) = excosx

A: Given: fx=excosx we know that ddxu.v=vdudx+udvdx                                              ..1

Q: Use a linear approximation (or differentials) to  estimate the given number.    1/4.002

A: Solution: A linear approximation (or differentials) to  estimate the given number.. 14.002  

Q: Crossover point The sequence {n!} ultimately grows faster thanthe sequence {bn}, for any b > 1, a...

A:   Given equation is  Multiplying by r on both sides    

Q: Use a Taylor polynomial of degree 4 to approximate the number √(1.1).

A:

Q: Evaluate the integrals

A: Since, our aim is to evaluate ∫0π2 5(sin x)32 cos x dx.

Q: In Exercises 3–8, compute f'(a) in two ways, using Eq. (1) and Eq. (2).

A: Given function is fx=x3+2x. Power rule of differentiation states that ddxxn=nxn-1. Differentiating t...

Q: In Exercises 47-60, solve the initial value problem.

A: we have to solve the initial value problem dzdt=t-32    , z(4)=-1

Q: Solve the exponential equation e4x + 5e2x - 24 = 0. Express the solution set in terms of natural log...

A: Given  e4x + 5e2x - 24 = 0

Q: The total surface area S of a right circularcylinder is related to the base radius r and height h by...

A: We have to find dSdt related to drdt and dhdt where neither r nor h is constant and total surface ar...

Q: Differentiate the function.

A: Given

Q: Show that the sine integral satisfiesthe (differential) equation xS'(x) + 2S''(x) + xS'''(x) = 0.

A: Given information: Sx=∫0xsinttdt To prove xS'x+2S"x+xS'''x=0

Q: In 1994, there were 714 violent crime incidents per 100,000 Americans. For the period from 1994 thro...

A: given In 1994  714 violent crime incidents per 100,000 Americans  

Q: ich of the following statements is not true? a) An n x n matrix that is orthogonally diagonalizable ...

A:

Q: Convert the following expression to the indicated base. 2x using base e

A: To convert the expression 2^x to the base “e” Suppose that, y=2x  

Q: Evaluate or simplify the expression without using a calculator.

A: Let the given value be y - y = ln1e6             ...............(1)y = lne-6y = -6lne               ...

Q: Solve each of the following word problems. Show your Solution. a. The admission fee at a small fair ...

A: To solve all these problems we have to convert these statements into equations.

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: the given integral is: ∫065dx25x2+36 we have to evaluate the given integral.   let the given integra...

Q: Write the standard form of the equation of the circle with the given center and radius : Center (0, ...

A: we have to write the standard form of the equation of the circle with given center and radius  Cente...

Q: Find the lengths of the curves. If you have graphingsoftware, you may want to graph these curves to ...

A:

Q: There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes ...

A: Given, Px≈x/lnx     ......(1) (a) find P(1000) put x=1000 in equation 1 P1000≈1000/ln1000or,p1000≈10...