y' = et ; y(0) = 2 find the general solution

Q: !. Find the numbers, if any, where the function f(x) is discontinuous. Explain your answer. x + 1…

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Q: 1+2 sec (Vx dx Į Va sin (/æ) tan (Væ) sin (/r sec (Vr and sec (Vx Hint: tan (yx =1. cos (Vx

A: Integration

Q: Which of the following is one of the correct steps to evaluate cos'x dx to obtain the desired…

A: Solving

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 6 cos(t)i + 6 sin(t)j+…

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Q: Descibe he moton of a partice with position y= 5 sin t; y=2 cos t as t varies in the interval - T, 5…

A: To find the motion of particle.

Q: 2.Find the indicated limit or state that is does not exist x* – y* C. lim (x,y)→(0,0) x² +y ху d.…

A: Solving

Q: dy Find the general solution of 2x² = a? + y? dx %3D

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

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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: 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: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

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Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

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Q: u+ 2v = 1+ vw; wy, and vw.

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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: 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: 2x + 1 Evaluate: (3x – 1) (x² + 2x + 2) 2 In (|3x – 1|) – In (x² + 2x + 2) + 4 arctan (x + 1) +C A F…

A: Find your answer below

Q: Q3 Find dy tan (X?y) tanx 2 y-(1+x)

A: A detailed solution is given below

Q: dx = x +C 3. 45x dx = -5x +C 4. 12V dx =-x+2x' +C 4x + 35x 4. 4 +8x dx = -5xi +C 4 28x 15x dx = 4x+-…

A: The integration of the integral  35x3/4/4 +8x-3.

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

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Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x? + 2x + 1…

A: continuty

Q: 9. If f (x,y,z) = 3x²y – xyz + y²z? _Ifind each of the following: fy (x, y,z) C.

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 Ju. (v x w)| to determine…

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Q: DO NOT include spaces in between characters. And, DO NOT include dy/dx in your answer. dy given x =…

A: Given - x=sin(x+y) Now we differentiate with respect to x  d/dx (x)=d/dx (sin(x+y))…

Q: Find the value of e which is defined as the angle between j+k and i+j_ None of the choices 4 프2 프3

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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: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: Evaluate the following and post your answers in t (Activity 2.1) 1.Sdz 2. Sa dx 3. S(7y6 + 8y3 –…

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Q: Let 1. f(x) x+1 Use the limit definition of the derivative to find (i) f'(-4) = (ii) f'(- 2) = (i)…

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Q: *) dx Evaluate:

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Q: :(7e*) cos (4e") dx Evaluate: e cos --cos (3e*) – cos (1le*) + C 22 ® os (3e*) +cos (11e)+c COS 6.…

A: We have to find value of given indefinite integral

Q: If f(x) = (2x) , find the derivative of the function Or) = f'(x) = 3(x)0.5 f'(x) = -(x)0.5 f'(x) =…

A: 1)f(x)=(2x) -0.5 2)f(x)=(1+sinx)/(x+cosx).

Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y = T9x2 + 16 %3D

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Q: x² +64 Using trigonometric substitution, given - dx, the simplified form of the integral is: sec ede…

A: ∫x2+64x2 dxput x=8tanθdifferentiate on both siddx=8sec2θ dθ

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: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

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

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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: (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: y = Vx* X

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Q: x² + 64 Using trigonometric substitution, given -dx, the simplified form of the integral is: x2 sec³…

A: Given: ∫x2+6464dx

Q: 9x 4. J, 16+9x

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

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Q: Find the minimum point for the function f(x) = 5x – 14x2 – 11x + 1

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

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Q: 3. Given the functions f (x) = a? - 4, g (x) = Va+ 4, and h (a) = %3D %3D | x + 2 find the DOMAIN of…

A: Domain is the set of all values  for which the function is defined.

Q: Find the equation of the tangent line and normal line to the curve ? = √? − 3 and whose normal line…

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Q: 2 2 y 6 L72 L48 yzdxdzdy =

A: Topic = Integration

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

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Q: In x25+x dx , we let x= 5sine.

A: ∫  x225+x2dx