Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

Q: 13. Calculate the divergence of the vector field F = x1e1 + 2x1e2 + +nx1en. ...

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Q: Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

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Q: ||r(t) × r"(t)|| Use the formula k(t) : to find «(t). %3D r(t) = e"i+e-tj K(t):

A: K(t)=?

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5) using the chain rule c) f(x) =…

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Q: x'y'y'+ xy' = 1 dy x' + y' dx 2ху dy 2 rv + 3v2

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Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: Find an arc length parametrization of r(t) = (e' sin t, e' cos t, le') r1(s) = (|

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Q: Find the particular solution that satisfies the initial conditic (e* + eX), f(0) = 1, f'(0) = 0 2…

A: Here we have to find the particular solution of given differential equation.

Q: Find div F and curl F if F(x, y, z) = xz°i+ 4yHx²j +42?yk. 5: 112. div F= curl F=

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: To find the volume of the given solid using triple integral.

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: Find the area bounded by the graphs of 1, y= and X=1 (Ao the right)

A: Find your answer below

Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

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Q: Find the general solution of the differential equation. dy = xy + 3x dx

A: To find the general solution of the following differential equation.dydx=xy+3x

Q: 2 _9 ii)lim- t-3 t2+4

A: Given query is to find the limit of the expression.

Q: Area A = 1,427 Calculate the definite integral f(x) dx by referring to the Area B = 2,460 Area C =…

A: Here we will find the definite integral,

Q: |r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = ei + etj 30 е4 K(t) : e-t (25 el2t + 1)

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Q: 7. Determine the following general antiderivatives. cos (x) dx -dx sin(x) а. - b. 10 sin(x)cos(x) dx…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it…

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Q: Find curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( i )k

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Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: A ferris wheel is 50 meters in diameter and boarded from a platform that is 5 meters above the…

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: dy If y = 3e5 . Find dz

A: Given query is to find the derivative of the expression.

Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

Q: Find the average value of f(x)= 4x - 5 from 1 to 3. ... The average value of f(x) = 4x - 5 from 1 to…

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: (d) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) = X…

A: Let's find.

Q: In(v¤) dædy 6. 15. Calculate ry

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Q: ,2 COS cos n Σ n3 n=1

A: Given problem:-

Q: -4 = ニ 200

A: To solve for x using the the given equation.

Q: (a²- x²}3½ dx

A: see below the answer and calculation

Q: Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x)=g(x)…

A: This question is related to Functions, we will solve it using given information.

Q: Find the general solution: y" + 4y' + 6y = 0.

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Q: x – 1 - V3x +1 lim Зх + 1 x→5 X – 5

A: Solution:

Q: Clear denominators in the following partial fraction decomposition and determine the constant B. 3x?…

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Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e-4x²…

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Q: - x = (y – 2)²

A: The question is a bit unusual, because, the given equation is not a cylinder.  Instead the equation…

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

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Q: Find the volume of the region enclosed by z = 1 – y? and z = y² – 1 for 0 < x < 21. V =

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables æ, y, z)…

A: Given problem:-

Q: у" — у' — бу %3D2, у (0) %3D 0, y'(0) = 0

A: Given can be written as (D2-D-6)y=2 The general solution will be y=CF+PI Complementary Factor(CF):…

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: For the function f(x)=2x^{2}+4x-1f(x)=2x2+4x−1, find the slope of the secant line between x=-1x=−1…

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Q: Calculate x sin(y)dxdy

A: On solving this we will get

Q: Find V × (V × F) if F(x, y, z) = 6xyj+ 4xyz k. V x (V × F

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Q: Find the e v

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Q: Determine the vector field of F. F(x, y) 3D 6і — 2)

A: GIVEN :                  F(x,y) = 6i - 2j.           ------(i)  We have to determine the vector…

Q: Find V x (V x F) if F(x, y, z) = 4.xyj+ xyz k. V x (V × F) =

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