A. Determine if p=9i-6j-24k and =(-15,10,40) are parallel, orthogonal or neither. B. Determine the direction cosines and direction angles for D= (-3,-1/4,1)

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A: A detailed solution is give

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A: Let's solve given integral.

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A: This is a problem related to taylor series expansion. Based on the general formula and concept we…

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A: Here we have to find the equation of plane

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A: Given : E = 104 Newton per Coulomb Force F is given as  F = qE

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A: Solution: P=u2+v2+w2   ............(1)Plug the value of u,v & wP =xey2+yex2+exy2

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Q: (3x² - 10)dx x² - 4x + 4

A: The integral using substitution is answered below:

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A: Let f be a function continuous on R and Fx=x∫0xft dt. Then to determine the expression for F''0.

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A: Given,  r→(t)=-4t4-3,-4e3t,-2sin(-t) ∫r→(t) dt =∫-4t4-3dt,∫-4e3tdt,∫-2 sin-tdt

Q: 5. Find the residues of the following: a. 2-2 z(1-2) at z = 0; at z = 1

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Q: b) Evaluate In x dx. X Question 3 For the differential equation y'+-- sin 2x, y (a) Show that the…

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Q: Calculate 14. lim (√x² + 1 - x). X18

A: Using series expansion about x =inf

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A: Here, the given function is: f(x)=53x So, note that ddx(ax)=axln(a) where a is a constant.

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A: Follow the procedure given below.

Q: 3.) КОЈ о dxdy

A: SOLUTION-

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Q: a) 4x²y - 3xy³ + 6x; d) e²x+3y; b) xy; e) x+y x-y c) xy²; f) 3x²y-7x√y.

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Q: e2-1 Evaluate: limx→0 2x²+x 01 O ∞ 00 O None of the choices 02

A: The given limit is: limx→0e2x-12x2+x   As we know that; The Chain Rule: fgx'=f'gx·g'x

Q: D) Find the parametric and symmetric equations of the line through the points (1,2,0) fic and sym of…

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