A spring has a natural length of 15 inches. A force of 10 Ibs. is required to keep it stretched 5 inches beyond its natural length. The work (in inch-pounds) done in stretching it from 20 inches to 25 inches is given by the integral 25 2x dx 20 15 2x dx 10

Q: Solve y' = y3 cos x (Show clear work!)

A:

Q: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of  B and C.

Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: 8. The (2*+1 – 2k) = %3D k=0

A:

Q: A right triangle has side lengths 3, 4, and 5 as shown below. Use these lengths to find tan M, cos…

A:

Q: Find the flux of F(x, y, z) = 4а, 32 + 2?, across the positively oriented surface 2 S given by R(u,…

A:

Q: Find the function value. If the result is irrational, round your Let f(x) = . Find f(2). 3 O A. 5 9…

A:

Q: 1 3c+6+2 J +3z+2 Evaluate:

A:

Q: rcos(x) d (32) Find the derivative: dx V1 – t2dt

A:

Q: 4. Solve 5x3 - 3x2 – 32x – 12 = 0

A: We have to solve the equation

Q: 1-2 For each of the following functions given by power series, find f'(x) and / f(x) dx. Do not find…

A: To differentiate and integrate the given power series.

Q: Direction: Find the antiderivative given the function J (5x + 2)´dx and its corresponding solution.

A: using integration by substitution

Q: (28) A particle is moving in a straight horizontal line. Its position, s(t), velocity, v(t) and ac-…

A:

Q: 1. Which of the following relations is FALSE. A) (ab)" = a"b" B) C) (a")" = a"* D)

A: Note: As per company policy we are supposed to solve only 1 question. So, kindly repost others.…

Q: PROBLEM 7: Find all eigenvalues and eigenvectors of A. [2 -4 4 A 3 -3 7.

A:

Q: Construct YOUR OWN example of how to determine the derivative of a given function and the process…

A: To write an example to how to find out the derivative and anti derivative.

Q: For each of the following, determine whether the expression is positive; negative; or zero. (You may…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Find the linearization L(x) of the function at a.

A: Use the derivative for finding the linearization of function

Q: Completely factor the polynomial f(x) = x +7x? + 10x.

A:

Q: ... Supply the missing integrand and the limits of integration -2 csinx dy dx _dx| %3D V1- y? 2 (x-…

A:

Q: Find the first term and the common difference for the arithmetic sequence. Round approximations to…

A: Use formula of arithmetic progression

Q: 8) Find the limit (exact value) a) lim Vy - 3y – y ytoo tan ax b) lim- x→0 sin bx (a ±0,b± 0)

A:

Q: e*(1-e*) (1+ x)[ In(1–x)] 12. lim, 0 'x0

A: Recall: If we have 00 form then we apply L'Hospital Rule.i.e, limx→a f(x)g(x)  = limx→a f'(x)g'(x)

Q: Test whether the differential equations are exact and solve those that are. I- y = %3D 2yt+1 -2xy…

A: Given

Q: 2. Define f, g: R → Ras if x 3 %3D and g(x) = 8x – 1. Flnd f •g and gof.

A: (fog) (x) = f(g(x))                = f(8x-1) =(8x-1)^2  if x<-1                                =…

Q: 3. Stickers. To celebrate the first day of spring, Lin is putting stickers on some of the 100…

A: topic- Lowest Common multiple

Q: 2. xy -(xy? cot Cans ☆ +y?)

A:

Q: 6) By implicit differentiation find a) xy + y´ = 2 find d´y/ dx² b) sin(x²y²)= x _find dy/dx

A:

Q: 1+ VI (20) Evaluate the integral: -dx. VI

A:

Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f (x) = L X→a

A:

Q: 2 0. ху dх dy -Vi-(у-1)?

A:

Q: Find the maximum and minimum values of the function f(x, y) subject to a + y* = 54 Maximum value:…

A:

Q: Find the angle between the line given by ⟨x, y, z⟩ = ⟨2t, 3t, t⟩ and the y-axis exactly.

A:

Q: た8e Ge whe'eh ー2x es ytural exponentioel frenebon / show all staps]

A: LetI=∫ 6e3x-8e-2xdxApply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdxI=∫ 6e3xdx-∫ 8e-2xdxTake constant…

Q: 1 çdt (5t + 4)2.7 (27) Evaluate the integral:

A:

Q: Given that sin a = and cos b = -, and a and b are in the interval , ), find sin (a + b) and cos (a -…

A:

Q: Evaluate the indefinite integral foan 2 sin“ v cos vdv

A:

Q: Find the area of the region enclosed by the curves y=x'and y = 4x. (Show clear work!

A:

Q: Evaluate the limit 25 – b lim b→ 25 5 – vb -

A:

Q: ... Supply the missing integrand and the limits of integration (Ух ӑx dy dy (4+y²) 3/²dy | V4+y?dy

A:

Q: 3) Graph the function over the specified interval. Then use the simple area formula from geometry to…

A: SOLUTION: As per given data, f(x)=3 ;[a,x]=[1,x] We know that, if we integrate function between…

Q: Find dy/dx by implicit differentiation. 12Vxy +4xyVxy –y dy/dx %D x – 2x²Vxy

A:

Q: Evaluate the limit In(x) lim x²-21x+20 X-1 X O a. 21 1 O b. -19 Ос. 21 O d. None of these. е. 1 19

A:

Q: Compute the indicated quantity using the following data. 12 sin a = 13 where = < a < T 2 cos B 3…

A:

Q: The two paraboloids z = x2 + y? – 1 and z =1 – x2 - y? meet in xy-plane along the circle x2 + y = 1.…

A: Topic: Representation of volume as triple integral

Q: 1 dA; R = {(x, y) : r² + y² s 4, r 2 0, y 2 0}. /16- r2 – y?

A: Using polar coordinates, integration is evaluated.

Q: 5) A cup of coffee cools at rate proportional to the difference between the constant room…

A:

Q: 2-the region bounded by y= .the x - axis.x = 2 and x = 3 is revolved about the y-axis find the…

A:

Q: Determine whether the vector field is conservative. If it is, find a potential function for the…

A:

Q: Question Given F(x) below, find F' (x). I o+2) di F(x) = Provide your answer below: F(x) = O…

A: