Use the appropriate limit laws and theorems to determine the limit of the sequence. an = 51/n (Use symbolic notation and fractions where needed. Enter DNE if the sequence diverges.) lim an =

Q: 3+ 4x2- -9х-36 3. у 3 4x2+28х+48

A:

Q: A. (1+ 4xy – 4x² y) dx + (x² – æ³) dy = 0 | - B. (y – sin? x) da + sin æ dy = 0

A: A detailed solution is given below 

Q: 2+x 5. Given f(x) =<tX Find X-4 %3D a) fe) b) f(a+1) c) f(x) + f(h)

A:

Q: 4. State the domain and range of the following functions. a) у%3D 5х —4 b) y= Vx-x c) ((x,y)ly = vx²...

A:

Q: sin x dx 2- cos²x CoS

A:

Q: Use sigma notation to write the Maclaurin series for the function. 2cosh x (2k)! 2 (2k)! (2k)!" 24+1...

A: Given : f(x) = 2coshx

Q: Use the ratio test to determine whether the series converges or diverges. If the test is inconclusiv...

A:

Q: et dx (9 + e2¤)

A: Integration   by subsitution technique 

Q: a) Enter a definite integral that gives the volume of the solid when the region above is revolved ab...

A: given problem is solved below in detail.

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

A:

Q: sec°(x) V cot(x) 6 X dx

A:

Q: Find all second order partial derivatives for the following functions: a) z = xe-2y +x In(y) + y ln(...

A: Partial derivative  In partial differentiation take only one variable and treat other as constant .

Q: Solve for the differential equation

A: Note: In the first question given equation is not clear as only left hand side of the equation is gi...

Q: Assume that f(x) = x. Evaluate a. lim f(r). f. lim (f(r)) – f(x)). b. lim エ→4 () g. lim (f(r)* +(f(r...

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Given: So, here an=1317n-1. Now,                limx→∞ 1317x-1=13·limx→∞ 117x-1=13·limx→∞ 1limx→∞ 1...

Q: 11. Use the definition of the limit of a function to prove that lim g(x) =- 6 if %3D (16x²-9 4x +3 3...

A:

Q: The form of the partial fraction decomposition of a rational function is given below. 16 – (x² + 10x...

A:

Q: The graph of f', the derivative of f, is shown below. Determine all possible inferences that can be ...

A:   ---------------------------------------------------------------------------- Key points: If f'x  ...

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A:

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and lengt...

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and lengt...

Q: Solve the given differential equation (3x-3y-2) da – (x – y+ 1) dy = 0 %3D | |

A:

Q: 1.) Find dy/dx. Given: x2 +y? = 25 2.) Find dy/dx. Given: x? + y = x³ +y? 3.) Find dy/dx. Given: x +...

A:

Q: Using IMPLICIT DIFFERENTIATION, find y'. 2ху + 3y y = 4x' – 5x'y Ах'у? + Вху + Сху - 24y? y'= Dx°y² ...

A:

Q: Sam's Smoothies serves many kinds of smoothies by blending fresh fruits and yogurt. Alex loves smoot...

A: Given query is to find the amount spend on smoothie.

Q: dx 9x2 - 12x-5

A:

Q: Find the inverse of the given matrix and verify if [A][A]-1 = [A]=1[A] = [1]: [25 5 [A] = |10 4 8 16...

A: Here, the given matrix is: A=25541051681222 First of all, find the inverse of the matrix.

Q: Evaluate the integral using trigonometric substitution. 1 dx xV1 + x6

A:

Q: Use the difference an+1 - an to show that the sequence | {n – 9"}+x Sn=1 is strictly increasing or s...

A:

Q: x3 , which Consider the plane region bounded by the curves y? intersects at point (0,0) and (1,1) Fi...

A:

Q: sin x 5 2 0, cos x

A:

Q: about the y-axis

A:

Q: D. (2x + 3) y =y+ y° (2x + 3) 2

A:

Q: Evaluate using substitution techniques

A: Given

Q: 1 d.r r/1+x°

A:

Q: Compute the first three non-zero terms of the Maclaurin Series for f(x) = sin-1 x

A:

Q: 14. Evaluate the following limits. a) lim (x² + 2x – 3) X-0 b) lim (x3 – 2x² + 3x + 4) X-

A:

Q: Glven the functions below, find dy/dx using CHAIN RULE. 2 y = 4t +1 ; ; x t = 3w + 4 5w - 2 Using th...

A:

Q: 27. Use the disk method to find the volume of the solid generated by the region bounded by the line ...

A:

Q: along the x-axis so that at time t 2 0, the acceleration of the particle is a(t) = 15Vr. ticle is 10...

A: In this question we will use basic concepts of calculus i.e concept of integration. We will use the ...

Q: 2. The daily number of calories needed by a reptile of weight x pounds can be approximated by the fu...

A:

Q: The wave heights h in the open sea depend on the speed v of the wind and the length of time t that t...

A:

Q: Here is a graph of the function f. Español Use the graph to find the following. If there is more tha...

A:

Q: х+1 3. J 25 – x²)3/2

A:

Q: A discrete random variable X has the following probability distribution: 3 4. 1 2 P(X) y 9 1. Find y...

A:

Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

A: We have to find the limit of the function along the path

Q: Find the average value of f (x, y) = = 4x cos(xy) over the rectangle R = {(x, y) | 0 < æ < n, 0 < y ...

A:

Q: Enclosing the Largest Area The owner of the Rancho Grande has 2,956 yd of fencing with which to encl...

A:

Q: Given the graph of the cosine function f (x) = cos x, evaluate the following limits: 27 ........ -1 ...

A:

Q: A. 2xydx + (y – x²) dy = 0 -

A:

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified...

A: