Using the integration bay parts formula with u = x- dv = cos x dx, the integral x cos x dx becomes

Q: Q1. Fill in the blank with a suitable mathematical expression. 1. The function f(x) is symmetric abo...

A: As per bartleby guidelines we only give first question answers. 

Q: Given the systems of ODE below with given conditions x(0) = 1 and y(0) = 2. dy + 2x dt dx et, 2y = 1...

A: First we find value of y in equation 2nd and put in equation 1st .  Follow step 2,3 . 

Q: 4. Given xo < x, and x, define x - xo X1 - X0 and let P1(x) interpolate the function f(x) at the poi...

A:

Q: Evaluate the integral [[(ate?) i+ (o-8) j+ (3) k]at 0. S[(t022) i+ (e-) j+ (3)kJat = i+ ()j+ ( )k (T...

A: The integral,      ∫014te2t2i+e-3tj+3kdt

Q: -6 -5 -4 -5- The plot above is created with the parametric equations S¤(t) = a cos(bt) ly(t) = c sin...

A:

Q: у 3 cos (4x — 19)

A:

Q: +o0 ΣΗ 1 -3 -1-n n=1

A:

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x...

A: Product  Rule of differentiation: du.vdx = u.dvdx +dudx.v dcos(x)dx = -sin(x) dsin(x)dx = cos(x) dxn...

Q: Find the first derivative of the given functions: 1.)  x=(Arcsinh(1-b))2   2.) y=e-xcosh ln(x)

A:

Q: +00 El-1)nInn- n=2 n2

A: The given series,        ∑n=2+∞-1nln nn2

Q: 18) rind fue indefinite inpagrel by ma uing tue Subs titel fion x=2Seco. af -de

A: The detailed solution is given below Thank you 

Q: esecx+lntanx -dp- 9. cos x

A:

Q: Using f(x) = In(3 – 2x), what is its f(n) (x)

A:

Q: 5xyz dv, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0, ...

A:

Q: Find the derivative of y = 3sin2x A 6 sin x B 6cos2x с) 6sec2x

A:

Q: Give the Maclaurin series expansion of f(x) = ln(3-2x). Determine its interval of convergence.

A: To determine the interval of convergence

Q: 8. f(x) = (2x - 3)(6x – 2)10

A:

Q: If u = e°", 3x dv = 4 sin 2x da then 3e* da, v = 2 cos 2x. Select one: O True O False

A: Let's find. 

Q: Using spherical coordinates to evaluate the triple integral zdV, where D= {(r,y, 2) E R : a s? +y + ...

A:

Q: Question 3 Find the change in y = 2x -3 if the x changes from 3.3 to 3.5. А) 0.1 0.2 0.3 0.4

A:

Q: Find (f-1)'(a) for f(x) = 4 – 4x when a = 12. %3D Enter an exact answer. Provide your answer below: ...

A:

Q: lim, s0¤(t) = 1? Оа. "+а — 0, z(1) — 2. 0, г(1) — 2. ОБ. — - 0, 2 (2) — 1. Ос. - 2г — — 0. 0, æ(1) 0...

A: To determine which of the following initial value problems has a solution xt.limt→∞xt=1a x'+x=0, x1=...

Q: 7 Type equation here.

A: topic - indefinite integral

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x...

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple quest...

Q: 1. Evaluate the integral JS aA, where R is the region: {(x,y)|0 < x < 1, –3 < y< 3] x²+1

A: To evaluate the integral: ∫∫Rxy2x2+1dA where R is the region (x,y)|0≤x≤1,-3≤y≤3.

Q: y' - y = 2x? 3

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next ti...

Q: Question 3 If lim an = 0, then the series a, is convergent. n=1 True False

A: Note: According to our expert guidelines only first individual question is to be answered kindly rep...

Q: Find the area of the surface obtained by rotating the curve y : sin x from x = 0 to x = 1.4 about th...

A: Given region bounded by y= sinx  from x=0 to x=1.4 

Q: Solve the differential equation (y3 – y?sinx – x)dx + (3xy² + 2ycosx)dy = 0 when x - 0, y = –1

A: Topic:- differential equations

Q: 3 Calculate the arc length of y = x? over the interval [1,5].

A:

Q: What is the integrating factor for the differential equation? dy dt + 9ty = ety

A: Comparing with dy/dx+p(x)y=q(x)  Then integrating factor=eintegration p(x) dx

Q: ( 2 + x², -2 <x< 0 4 f(x)dx; f(x) = 1 ·x + 2, 1. 0<x< 4 -2

A: ∫ xn dx = xn+1n+1 +C ∫ab f(x) dx = ∫ac f(x) dx + ∫cb f(x) dx , where , a&lt;c&lt;b.

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

A:

Q: B Graph the follo wing y, = 2sec2x %3D Yz = 1-25in (x+ ) Y3=2 cotx

A: We know, sin(x+π/2)= cosx Given functions, y1 = 2sec2x y2= 1-2sin(x+π/2) y3= 2cotx

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the y-...

A:

Q: The half-life of cesium-137 is 30 years. Suppose we have a 130 mg sample. (a) Find the mass (in mg) ...

A:

Q: If x? + y? = 100 and dy 8, find dt dx when y = 6. (Enter your answers as a comma-separated list.) dt...

A: Given that x2+y2=100dydt=8To find :dxdt when y=6Solution:x2+y2=100x=100-62=8x2+y2=100Diffranciate w....

Q: This exercise uses the population growth model. A culture starts with 8300 bacteria. After 1 hour th...

A: Since you have posted multiple questions I can do first question as per our company guidelines pleas...

Q: Show detailed solution for all. a) Provide the Maclaurin series expansion of f(x) In(3 – 2x) b) Find...

A:

Q: ∑ n=1    1/9n^2-18n+8

A: Given ∑n=119n2-18n+8Now lets substiute n=1 and solve

Q: d'y Find for x* +y* = 16. Express your answer in fully simplified form. dx?

A:

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm³/...

A: Let the radius of the sphere is r then given drdt=4 mm/secand diameter is 2r=40 mm

Q: ( 2x-sy+12) dx +(7x-4y+15)dy = o 2,

A:

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

A:

Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y)...

A:

Q: 1. f (х) — 5ӕ -4

A:

Q: A conical tank of water, 10 ft high with radius of 6 ft, is leaking at the bottom at the rate of 10 ...

A:

Q: tan x[cot x – cos x]dx |

A: Topic:- integration and trigonometry

Q: Show detailed solution for all. a) Provide the Maclaurin series expansion of f(x) In(3 – 2x)

A: Here we have to find the maclaurin expansion of the given function.

Q: Find (and simplify) the equation of the tangent line to the graph of

A: Equation of Tangent line to curve y=3xx-1, at x=2