Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i + 11 sin(t)j+ 4tk; t = NOTE: Enter the exact, simplified answers. V4961 41 V41 K = 41 V41 V4961

Q: integral is true or false: 3 dxdydz = 72. 0. 1 -3 Select one: Truo

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Q: Find the equation of the tangent line to the curve y =4x-8 at the point (3.-2).

A: Topic = Derivative

Q: x2 In solving for the antiderivative of f(x) = Fusing trigonometric substitution, Jf(x)dx is…

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Q: dy Find if yJx-9 =Xyt2 %3D

A: we have to find dy/dx

Q: Reduction of order can be used with 2x to find a second solution for the %D DE: 2x²y" – xy' - 2y =…

A: Given y1= 2x² is a solution of 2x²y''-xy'-2y=0....(i) So 2x²y1''-xy1'-2y1=0....(ii) Let y=…

Q: The graph of a function f is shown below. YA f a Graph b 1. Which grap is an antiderivative of f?

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Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

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Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 1 - x dx 2. y =

A: To evaluate the given integral.

Q: S sec?x csc²xdx O None of the choices tanx + cotx + C O - tanx + cotx + C O - tanx - cotx + C O O

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Q: Q3) Evaluate triple integral f, L(x - y?)dz dy dx.

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Q: (x – y)dr + xdy = 0.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: "u,V.w are three vectors such that each is incined at an angle of 4 with the other two, and that lul…

A: To find the scalar product of two vectors with the given conditions.

Q: dy Given 4x -9y =1. Find by implicit differentiation. dx

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Q: Evaluate triple integral f, SE Lx? - y?)dz dy dx.

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Q: (4x* – r*y +y*)dx + x*dy = 0.

A: Let's find.

Q: Question 6 The tangent to the curve y = 1/x intersects the r-axis at (/2,0). What is its…

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Q: 9- 4x2 Evaluate: xp-

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

A: To find particular solution of D.E.

Q: 1 et dx 1 (1 — е*)2

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Q: S sin²x cos²x dx 1 sin 4x + C 32 O A none of the choices 1 1 ;sin 4x + C 32 8*+3, sin 4x + C O B

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Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1

A: ∫xdxx-1

Q: 5.Find all the first partial derivatives of each function f (x,y) =(2x– y)* а. 3/2 S(x, y)= (4x–…

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

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Q: dx :Ja-4)(x-1) Evaluate: 1 A (x-1) + C X- 4 B None of the given choices x- 4 + C х-1, © 3ln

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Q: The shaded region R is bounded by the lines x = 0, y = 0, and the curve y = x² – 2x + 2 as shown in…

A: Here, the volume is: V=∫03π(y)2dx =π∫03x2-2x+22dx=π∫03(x-1)2+12dx

Q: Question 9 In Sx²/25+ x²dx , we let x= 5sine. (A) True (B) False

A: If x=5sinθdifferentiating On both sides.dx=5cosθ∫x225+x2dx=∫(5sinθ)225+(5sinθ)25cosθ…

Q: Evaluate the triple integral. SSSE2.xy dV , where E lies under the plane : = 1+x + y and above the…

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Q: Determine the area of the circle whose center is at the origin and tangent to the parabola y = x2 -…

A: y=x2-100from the grapph attached, Parabola cuts X-axis at (10,0) and (-10,0)

Q: irvature and the radius of curvature at the stated poi r(t) = 6 cos(t)i +6 sin(t)j+ 7tk; t= 2 r the…

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Q: dx 1.4 Ven(3)+2x dx 1.5 Show steps. Your reasoning is more important than the numerical answer.

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Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: Option A is true

Q: Evaluate (s 2'ds Oa 2 1) In2 Ob. 2 (sln2 - 1) (In2)2 O. 2(sin2 - 1) (In2)2 Od 2° +1) In2

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Q: dy Find given x'+y' =8xy. dx Note: Enclose all terms in a parenthesis if either the numerator or…

A: Here, the given equation is: x3+y3=8xy...(1)

Q: Evaluate: | (cosh²2r+ sinh²2r) dr (A 2r +C 1 -sinh 2r +C 2 B -sinh 4r +C 4 D r +C E None

A: cosh²(2r)+sinh²(2r)= cosh(4r) ∫cosh(x)dx= sinh(x)+C, C is a constant.

Q: 4.Describe the largest set S on which it is correct to say that f is continuous S (x,y) = In(1–x² –…

A: Given problem:- Describe the largest set S on which it is correct to say that f is continuous C.…

Q: Evaluate: / y6 sech(e7hny) tanh (e 7Iny) dy A) -sech(y?) +C 7

A: We know that    elnx=  x we use above result to determine the integral

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 1 1 lim ttoo\ 6t2 +7' 5t (?, ?)

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Q: Jse the vectorized Euler method with h = 0.25 to find an approximation for the solution to the given…

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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: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydx (8r+7)dudy O none of the oices

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Q: Question 8 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. (A True…

A: We can evaluate the given integral by using the substitution u = csc (5x)

Q: 2 3) -2

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Q: Find all values of x that satisfy the equation f'(x)= g'(x) it f(x)= sin x and g(x)= cos x. 3T +k T,…

A: We can solve this as follows:

Q: R={ (x,y): 0<x, 0<y, x²+y? <9} be enclosed region. The result of the following double integral (by…

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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: Work Problem 1 (With integrity statement] Let R be the region bounded by yx+ 2, y=0, und x=2. Draw…

A: To find the value of given double integral.

Q: In XVX2-625 dx , if we let x-25sece, then dx = 25secede. A True B) False

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Q: 24. dx AX

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Q: A ladder 9 meters in length is leaning against a vertical wall on level ground. As the bottom end of…

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Q: The general solution of the second-order linear homogeneous differential equation y" +6 y=0 is y=…

A: Let's find.