x + 5 Let f(x) = %3D x + 6 f'(x) = %3D 8.

Q: Define the role of partial differential equations in real life. Do you have encountered some…

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Q: ction f(x)=-

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Q: ● f sec³(x) dx ● ► f sec¹(x) dx • f sec³(x) dx MTH 32

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Q: tionship between x and y.

A: Linear Eq: 9.x=1,2,3,4,5y=f(x)=2,4,6,8,102y=xSo, this is the requiredequation of line.

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

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Q: y=-sec^-2 (In x)

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Q: 1) lim y-4 x+6x+5 2) lim 2-3x-4 t+3t2-12t+4 sin3h-2h 3) lim 4) lim 3-4 gin

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Q: Find j Partial derivative

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 9) Find all relative extrema in the interval (0, 2π) for y = x - cos x

A: Here we have to find the relative extrema.

Q: 2х -1 dx Integrate dx by using substitution method. e*-x+1

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: ftan (x}sec"(x)dx Scot (x)csc°(x)dx Ssin (x)cos°(x)dx

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Q: •tanx √1+1² 0 1+e' sec ³x 1+etanx If f(x) = A B C D -dt, then f'(x) equals 1+tan²x 1+e' tan.x In…

A: Solved below

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

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Q: Leb Fur =ue Show thab f6/0 )c

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Q: V3x-e2x-(x ln x)(ln(ln x))| In(ln x) Given a function, y = dy Show that dx V3x-e2x (x In…

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Q: Using Beta function, show that dx 3- (b – x) (x – a) |

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Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: Verify the identity.

A: Given: arctanx=12arctan2x1-x2. The interval given is -1<x<1. From the given interval, let…

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 6. Use implicit differentiation to find first order partial derivatives: tan-(x²y) = y²z3 +…

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Q: 8. y = -5 e3x^2, 2nd derivative 9. y = 7 In 7x, 2nd derivative 10. y = -3 cot 2x, 2nd derivative

A: Question 8,Given,            y=-5e3x2To find : Determine the 2nd derivative of the given function.

Q: II. DIFFERENTIATION 1. (E- 2x) = A- 2 B.는-2 +2 D.-2 %3! 2x 2x-1 2. 21

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Q: First and second derrivative of y= 2 Arccos(1-x/2)+√4x-x^2

A: Given, y=2cos−11−x2+4x−x2

Q: sin x 8x y%3= 8x sin x dy COS X %3D COSX dy COS X 8. %3D 8. COS X dy O dx X COS X + sin x %3D 8 sin…

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Q: Part III - SOLVE the following DIFFERENTIAL EQUATIONS * for partial derivative symbol, use the…

A: The solution are next step

Q: 3. y = (- at x= 3 x+1

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Q: ■ Find y 2    implicit differentiation.   x3 + y3 = 1

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Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

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Q: 13. dx √ex-1

A: Given: I=∫dxex-1   ...1   As we know that; The Chain Rule: fgx'=f'gx·g'x And ∫1x2+1dx=tan-1x+C

Q: 10 If f (x) dx -7 and f (x) dx = 1 then determine -3 -3 10 [1- f(2) dz 5 showing working.

A: Given: ∫-35f(x)dx=-7 and ∫-310f(x)dx=1

Q: Derivatives of y = 3x²(x² + 1)³

A: We can find the derivative as below.

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: a²u Q15// Solve the partial differential equation дудх tan-1x sin³y ди given that = y when x = 0 and…

A: Given: The partial differential equation is ∂2u∂y∂x=tan-1x sin3y , given that ∂u∂y=y when x=0,u=1…

Q: tanx If f(x) = (Α) B C D S 0 sec ³x 1+etanx In (secx) √ 1+tan²x tanx 1+e sec²x 1+ etanx 1+1² -dt,…

A: Here, given that: f(x)=∫0tan x1+t21+etdt...(1)

Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

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Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

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Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

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Q: 1-2 c) dx

A: Evaluate the integral: ∫01e1-xdx. Simplify- ∫01e·e-xdx Apply ∫afx dx = a∫fx dx here a is constant.…

Q: 3 √√√x tan-¹ √x dx 1. 1 2. T 3. 3x² + 4x³ +16x² +20x+9 (x+2)(x²+3)² 1 12x+5x+3 4. 0 √ sec¹ x tan³x…

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Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

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Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: f(x) = VT cos x2 COS 2x f(x) = x² + 4

A: Given functions is, f(x)=xcos(x2) So, differentiating it with respect to x, we get,…

Q: 3. f(x) = 6xi – 3x ; x € [- 2,1 first derivative critical numbers stationary points End Points…

A: Here, the given function is: f(x)=6x53-3x23; x∈-2,14

Q: f(x) = tan (2x5 – x) %3D f'(x) = 9хcosx f(x) = %3D csc(x) f'(x) = %3D f(x) = ex f'(x) = %3D e5x+3 y…

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Q: differential

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Q: (a) Give two reasons why it is important to study analytical techniques for solving partial…

A: We shall solve first question only as per the company guidelines. For others kindly 1 post again by…