Give the parametric and symmetric equations of the line that passes through the point (4,-3, 5) and is perpendicular to both vectors (2,6, 1) and (1,3, -5).

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

A: I am attaching image so that you understand each and every step.

Q: 1 * cot³. CSC2 x3 x2

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Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: + c2e4x The auxiliary equation of a second-order homogeneous linear differential equation is m - 7m…

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Q: The limit below represents the derivative of some function f(x) at some number a. 3(3 + h) - 243 lim…

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Q: a. Draw the funclion y=a/ %3D

A: Find your answer below

Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

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Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: 1 In solving the antiderivative of f(x) = 2 - sin(x) by miscellaneous substitution, the substitution…

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Q: applying substitution méthöd: sqns -48

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

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Q: a. f(x) = 4x + 11 find: f'(-2) b. f(x) = 2x2-5x 3 find: f'(2)

A: Given: f(x)=4x+11 f(x)=2x2-5x-3

Q: S xdx can be solved by either algebraic subsitution or integrataion by parts. Vx- 1 A True B False

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Q: S sec°x tan x dx +C + C sec³x + C

A: ∫sec5x tanx dx=∫sec4x (secx tanx) dxusing formula∫fn(x) f'(x) dx=fn+1(x)n+1 +cHere , f(x)=sec4x ,…

Q: 1 In solving the antiderivative of f(x) = by miscellaneous substitution, the substitution z =tan|…

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Q: (a) Find the unit vector having the same direction as B- A+ 2C. (b) Give the direction angles of B-…

A: We have to solve given vector Questions

Q: Let a = (1,2,3),b = (4, –3, –1),c=(-5, –3,5) and d = (-2, 1,6).Find: %3D а. а+ 5b b. [7c| – |5d| c.…

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Q: Evaluate f Vr+ V?dx Oa. 3 am +2) +C (V2) +C can) Ob. 2 am +2) +C 30 om +C (25) Oc 2 an +m) +C O d. 5

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Q: Find the derivative of the function f(x) = csch () () -2 coth csch 2 2 -2x coth csch -x coth csch 2…

A: L

Q: Let y=f(x).Which of the following correctly defines dx [fk+Ax)-fw] a. lim Ax+xL Ax Ob. lim Ax+x…

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Q: 9 – 4x² -da | Evaluate: (A) f (x) = V9 – 4x² + 2 sin () +C B None of the given choices f (x) = /9 –…

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Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: Determine the general cquation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

A: We have to find equation of ohm plane

Q: Find the derivative of f(x) = -2x Or) - 6x2 Of (x) = -6 x2 Of (x) = -6 x3 %D Or-6x* f (x) = 6 x4 %3D

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Q: find the rational number represented by the repeating decimal. 0.451141414

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Q: In solving the antiderivative of f(x) = 2- 3sin(x) by miscellaneous substitution, the substitution…

A: The function f(x)=12-3sin(x)

Q: tan5 e -y secseс е-У 9. S -dy ey

A: Since, the student has asked to solve question number 9, so we are going to solve only question…

Q: To evaluate sin 0 do , factor sin*0 as (sin²0) ² sin® and let sin²0 = -(1- cos20). A True В False

A: To evaluate: ∫sin5θdθ Let I = ∫sin5θdθ ⇒I = ∫sin4θsinθdθ

Q: Which of the following evaluates the double integral xy dA,

A: We can solve this as follows:

Q: x- 2 For the function f(x) = x-5 a. the graph of the function is until x = 2 only. O b. the graph of…

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Q: Evaluate the definite integral. e12. i+ k 12 e12 i-elj+; k 12 e12 -1 12 e12. k 12

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Q: 3 3. Given the graph of the function ƒ(x)= (x+2) a. Give a step-by-step explanation of how to graph…

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Q: 1 In solving the antiderivative of f(x) = 3sin(x) + 4cos(x)+ 5 by miscellaneous substitution, the…

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Q: Q3) Find the Area bounded by the curves y? = and x = 2y – y².

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Q: Find the values of a and b for the curve x'y+ay =b if the point (1,1) is on its graph and the…

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Q: If D is the region in the third quadrant between x +y? = 1 and x2 + y? = 4, then using the polar…

A: We have to convert given double integration into polar coordinates integration.

Q: Q3) Evaluate triple integral f x - y²)dz dy dx.

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Q: DO NOT include spaces in between characters. * Find the value of at the point (0,1) given the curve…

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Q: dz In Vz+4 - 2 2ydy , if we let y=Vz+4, then the new integral becomes у-2 A True B False

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Q: A line is drawn through the point (6,4,2) perpendicular to the yz- plane. Find the coordinates of…

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x? y = dx %3D x2 + x – 2

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Q: cos 2x sin'x dx can be evaluated by factoring sin x as (sin?x) 2sinx and transform sin?x into 1-…

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Q: Evaluate the triple integral xyz dV, хуz R

A: Follow the procedure given below.

Q: Find the value of A which is defined as the angle between i+j and j+ k.

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Q: 2. Suppose that the edge lengths r, y, and z of a closed rectangular box are changing at the…

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Q: Given In.ry+x+ y =2. Find dy by implicit differentiation. dx

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Q: If u.v.w are three vectors such that each is inclined at an angle of " with the other two, and that…

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Q: Q3) Find the Area bounded by the curves y? = x and x = 2y – y?.

A: The given curves are; y2=x &amp; x=2y-y2   Now find the point of intersection between the curve y2=x…