2. Find the local and absolute extrema for the following functions: (a) f(x) = x? + 2/x on [1, 4]. (b) f(x) = r/2 - x3/2 on [0, 4). (c) f(x) = sin x + cos z on [0, 27). %3D a. fN= x?+2/x 2x2 2.

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge-Kutta method, what is…

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Q: (i) Integrate the following functions with respect to x: 7 y =- 4x 2x - 3 y = 2 y = x* sin (x° +1)

A: Explanation of the answer is as follows

Q: g) y ext= cosh x + √cosh²x -1 +7 ex е X h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy dy -…

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Q: 2 S (x) + x³)dx = ? -1

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Q: Find the most general antiderivative of the function g(x) 3x2 -e + coS I | O 6x-ex-sin(x)+C O…

A: The given function,  g(x)=3x2-ex+cosx  .................................(1)

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

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Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: 1. S (5x-12) dx 2. S x³-6x² +8x 3. S -(3 cos² 0 +8 cose-12) sine de cos³ 0+7cos² 0+ 12 cos 0 dx…

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Q: (4)Evaluate the definite integral (a)[ 1+sin x dx (b) | 2t + cost dt -7/2 5 x + dx (d)[ sec' 0 d0…

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Q: 113. Suppose that F(x) is an antiderivative of f(x) = (sin x)/x, x > 0. Express sin 2x dx х in erms…

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Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: Solve the problem. Integrate f(x, y) = sin(x2 + y2) over the region 0<x2 +y2< 100. O T(1 - cos 100)…

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Q: Find extrema of the following function over the given intervals: a) f (x) = 4x –15x² +12x+7 over…

A: Since, there are multiple questions in one image, we will solve the first two parts (a) and (b) for…

Q: Match functions ƒ with their antiderivatives F. F (x) = cos (11 – x) F (x) = -11 cos (x) F (x) = -…

A: use substitution method and product rule for finding the antiderivative.

Q: Given (1+ 3x sin y) dx – x² cos y dy = 0 with y(1) = 0. Using Euler or Runge – Kutta method, what is…

A: Given 1+3xsin ydx-x2cos y dy=0....(1) with y1=0 We will find the value of fx, y to approximate y

Q: 4. Supposea function y = f(x) is so be revokved at x = e from point (a, b) to (c, d), what is the…

A: Please refer the attached image for complete solution.

Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In () (Inx)2+ (In Vx)3 3* 2) y = tan-1 (x*)

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Q: 3. The function 0(x) = 1/ sin(x) is an integrating factor of (ysin(x) + cos(x))dx + (x+ y) sin(x) dy…

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Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: 12. Show that F(x) = sinx – x cos x+2 is an antiderivative of f(x) = x sinx.

A: Given, F(x)=sinx-xcosx+2 To show that the above function is an antiderivative of f(x)=xsins.

Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

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Q: 1.) Find the equation of the line tangent to f(x) = 6 ln(7– 3x)+5e-4 – 6x – 2 at x = 2 2.) Find the…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: 1- Find the average rate of change for y = xo = 1 x, = 2 2- Find the instantaneous rare of change…

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Q: 2. In(x + iy) = A. cos(x) cosh(y) - i sin(x) sinh(y) B. sin(x) cosh(V) + i cos(x) sinh(y) C. cos(x)…

A: solution

Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: 6. The coefficient of Sin(x) in the antiderivative of F(x)=| is

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Q: Q.4 Find the most general antiderivative of the function 1) f(x) = 2x + 1 2) f(x) = cos2x + sin3x…

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Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x 6 Sketch the region bounded by the…

A: Solved below

Q: 2. Evaluate the following: 1 - dt 1+t? d ctanx а. dx 2 b. f(8-2x) dx x' +1 dx x+1 С. 3. Evaluate the…

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Q: g) y² ex+y = cosh x + √rosh²x -1 +7 et h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy Sin 2x…

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Q: 1) In this problem, let * = 2, the value Ar = dx, dy = f ' (x)dx, and Ay = f(x + Ax) - f(x) to…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: dy Find if y = ln x5 + e-cos 2x – In e?. dx dy 5 ,cos?x-sin2 x dy 5 4 sinx cos x = - dx e sin2x-cos2…

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Q: 1. S(tan -1)ʻ dp 2. sin2 B cos B dB .5 xdx 3. S (-7-8x-x* 4. Sx³ (a2 + x2) dx xdx 5. f (x²+a²)³ 6.…

A: (2)

Q: Find the most general antiderivative of: f(x) = 4√x − sec(x) tan(x) + (7/(x2+1))

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Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: Find the most general antiderivative of: f(x) = 4√x − sec(x) tan(x) + (7/x2 +1)

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Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: y=sin-1x

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Q: use the integrating-factor method

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Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

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Q: 7. (cos x+xcost)dt +(sin t -t sin x)dx = 0 Ans. t cos x+x sint c 8. (ysin x+xy cos x)dx +(xsin…

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Q: 4- Find dy/dx for y = 3(sin-(e-3x²))2 dy 3[(sin-{(e-3*)i* In3 2(sin-1(e-3**) - 3x2 1(-6x) dx V1-…

A: Differentiate term by term

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge - Kutta method, what is…

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Q: 10. * S sin(In x)dx 1 C x sin(Inx) – cos(Inx) + C 2. x sin(Inx) – cos(lnx) + C 1 x sin(lnx) +…

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Q: s the indefinite integral | x2 cos(x3) dx becomes 1 cos(u) du- must also convert the integral…

A: Given query is to find the integral limits.

Q: Question 2 Set up an integral for the length of the curve y=V1+x? on 2 sxs3. x2 1+ dx 4(1+x)3/2 x2…

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Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu