Use the limit comparison test to determine if the series converges or diverges. 00 8. 23) E 8 + 9n(In n)2 n = 1

Q: Use series to approximate the definite integral I to within the indicated accuracy. 1/2 x arctan(x)…

A: We have to find the value of integral.

Q: y x/x, x-4, and y =0 -2

A:

Q: 18. Find xV4x -3 dx 18. SxV4x - 3 dx

A: Use substitution to solve

Q: Step 1 |an + 1 an + 1 n+ 1 1, or lim = 00, then n00 an Sa, diverges. For any fixed value of x such…

A:

Q: Find the area of the shaded region. y = x² +1 %3D 5 y = x -1 A 23 2. 2/2

A: Given

Q: r0.5 .2 X- dx (lerror| < 0.001)

A: Given I = ∫00.5 x3 e-x2 dx =− ( x2 + 1 ) e-x220.50

Q: Finding the length of a curve. Arc length for y = f(x). Let f(z) be a smooth function over the…

A: To find the arc length of given function.

Q: 9. (D² - 1)y = 2/(e – e-*).

A:

Q: Evaluate the definite integral. + ej+ dt - 1) i - (e" - 1) j +k O e? i+ (e-1-1) j+국k 2.

A:

Q: Find the nth term of the arithmetic sequence (a wh a, = 4; d = What is the nth term of the…

A:

Q: Let F(x) = f(x*) and G(x) = (f(x)). You also know that a' = 5, f(@) = 3, f'(a) = 13, f () = 1 Then…

A:

Q: Problem 3. at a speed of 60 cm/s. Suppose the function g models the radius as a function of time t…

A:

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

A:

Q: S V9x² + 64

A:

Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

A:

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

A:

Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

A:

Q: Consider F and C below. F(x, y, z) = (y²z + 2xz2)i + 2xyzj + (xy² + 2x²z) k, C: x = Vt, y =t + 8, z…

A:

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A:

Q: Find the equation of the tangent line to y=(3x+4)3 at the point where x= -2

A: here given y= (3x+4)3 slope  of the tangent line is y'    Here y' = 9(3x+4)²   Value of y at x=-2 is…

Q: A farmer finds that if she plants 90 trees per acre, each tree will yield 30 bushels of fruit. She…

A:

Q: differential cgnatuin as A. Identify the given to the dependent variable, degce z the eguati degre 3…

A:

Q: Find the slope of the polar curve at the indicated point. TT 7) r = 5 cos 30, 0 =

A:

Q: Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5…

A:

Q: Which of the following is a parameterization of the line that passes through the point (1, –3) with…

A: First frame the equation then verify all the given option.

Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 5 sec2 x dx -T/6

A:

Q: Find the area lying outside r = 6 cos 0 and inside r = 3+3 cos 0. Area =

A:

Q: Given sin 0=- determine all possible values of 0 over the interval [-2n, 2n]. 2'

A: Given query is to find the value of the Indicated angle.

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

A: Given query is to find the series converges or diverges.

Q: Evaluating Indefinite Integrals - Partial Fraction Decomposition Suppose we want to evaluate the…

A:

Q: Write the equations in cylindrical coordinates. (a) 3x² – 6x + 3y2 + z² = 5 z = 7x2 – 7y2

A:

Q: fF(x)dx = -9 and Si (x)dx = . 3 tind f(x)dx Given that

A: We can solve the answer using the properties of definite integral as below.

Q: -2

A:

Q: The letters r and 0 represent polar coordinates. Write the given equation using r-4 cos 0 Complete…

A:

Q: Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8…

A: Here We have to use the definition of the derivative.

Q: 3. If f(x) = [ 8+f dt ,find f'(1). .

A:

Q: Setup the iterated integral using the order dydx and dxdy. Sketch R. // (Va+ e") dA where R= {(x, y)…

A:

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: Determine convergence or divergence of the alternating series. 24) E (-1)n 6n5 + 5 n = 1

A:

Q: dy (1- y)

A:

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: Ay (2, 4) y = 2x y = x2 2. Using a vertical element of area, the area of the shaded region is given…

A:

Q: (H.W) 1- Solve by choose M this time (2 x y² + 3 x² ) dx + (2 x² y + 4 y³ ) dy = 0 2- Find the…

A:

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

A:

Q: A. (, 글) %3 ( B. (- , -) =(

A: We will find the coordinates in polar form.

Q: A job applicant estimates that his chance of passing a qualifying examination is , and his chance of…

A:

Q: Find the angle between vector [2, −5,7] and the x-axi

A: topic- angle between vector and x axis

Q: If S; (x²-1)(2x-x*) dx can be resolved into A S+ B S f(x)dx + D S g(x)dx , then x²+x-2 lim, ° dx +…

A: Partial fractions: The fractions needed to decompose a rational equation are called partial…

Q: 3. Find the binomial series for (1+x)3 4. Use the result in problem 3 to give a power series…

A: