3 Find f(x) if f'(x) = and f = 1. %3D O A. -4 X- +13 4* B. -4 X- -4+C OC. -4 OD. х + 13 4/5

Q: d Evaluate the following derivative: dx (1 + t² dt. Oxv1 +x4 + v1+x² Main Content None of these O…

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Q: Q.2 Evaluate I = f* x*(1 - √x) dx using Beta-Gamma functions.

A: Given: Integral I = ∫01x4(1-x)5dx We have to evaluate the given integral using Beta Gamma function.

Q: 2. Evaluate the following ~2 1 (i) T dx 4x+1 cln4 -2x+1 dx e (iii) S, x?e-3x dx 1

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Q: 12. Given: f(x)dx = 4 S(»)dx = -1. and Find: (a)

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Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

A: Given y=e12x+3xe+e2e Given query is to find the derivative y'

Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: 4 the second order For the function y = 4 e" - - d'y is derivative dx? 4e + 8x-3 O 4e" + 4x-2 -3 O…

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Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: 8. 4S f(x) dx = dt 9. S f(t) dx d 10. dx | f(x) dx = a

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Q: 1 What is S dx? x²+2x+5

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Q: -2x y" + (e by = 0 (e-* = z) -

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Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A: Given: ∫kx4+x2dx We have to evaluate the given integral.

Q: and 10 g(x) dx = 14,   0 find 10 [2f(x) + 3g(x)] dx.   0

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Q: 51. The functions y = e* and y = x³e do not have elementary anti- derivatives, but y = (1 + 3x)e"…

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Q: 2. Find by implicit differentiation. dy dx 4 (a) x +xy +y = 5 2 2 3 =D5 3 2. (b) x- xy + y 3. =D1

A: Recall: An equation of the form f(x ,y)=0 , in which y cannot be expressed directly in terms of…

Q: -Arctan2(3e") = dx ke*Arctan(f(x)) g(x) . Compute kf(0) - g(0) – 3 Let A 5 В) з C) 4 D) 2

A: First we are going to calculate derivative and then comparing with given to find out the required…

Q: Given そ< fcx)59 for S5 xs6 estimate the volue of s f cx) dx 5. S. foo dx s

A: Here we will have to find out the upper and lower limits of the integration for the given limit of…

Q: 18 12 f(x) dx – | f(x) dx = f(x) dx - where a = and b =

A: Find value of a and b.

Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: 1₁ f(x)dx = 6 ln([x]) - 6 ln(|x]) — -—-cos(5x). -cos(5x) - 3e + x² + 6x + C

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Q: 90% of it Suppose dy/dx = x-y and y = 2 when x 1, Use Euler's Method with increments of Ar = -0.1…

A: Given the differential      dydx=x-y with y(1)=2. Find y(0) using Euler's method with step size…

Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-7)dx…

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Q: X = e not inelude th degreo QUmbelin

A: The triangle is shown in diagram ,

Q: (-4x-12) dx For J x+10)³ (x-4)³ F(x) – 1. What is F(3)? -

A: Given: ∫-4x-12x+103x-43dx=Fx-1   ...(1)

Q: 1. Find dy dx S(x)= e**/2x-5 (6-5x)* (iii) f(x) =

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Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: Evaluate the second derivative of e22.1.png а f(x) acos(b/x) x2 if a = 345 and b = 0.6 at x = 5…

A: Given: Let us consider the given, fx=acosbxx2 where a=345 &amp; b=0.6 at x=5 using BDA with ∆x=0.06.…

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: d S[e-In(2t+1)]dr. find g(x) - dx A e-In(2x+1) 2 B (2x + 1)² (2x + 1)² (2x+1)² If g(x) = D

A: We have to find out the derivative

Q: x - 3 7. S V25- (x-2)2 dx 8. S tan5 (2) dy

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

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Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

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Q: 2. Suppose that . f(x)dx = 9 and S g(x)dx = 4. Find the exact value of 2f(x)dx.

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Here we can use the following formula  If z=fx,y, thendz=fx dx+fy dyδzδy=fx δxδy+fy

Q: dæ4 evaluated at x = -1 dx evaluated at x = –1 dx? evaluated at x = -1 dx3 dªx4 evaluated at x = -1…

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Q: dy for e dx (*² +1), 6. Determine ln( 19) + x² – xy =

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Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: Q5; Use three iteration of Picard's method to solve dy = 3x+ y when x=0.1, given that y 1 dx for…

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Q: .5 If f(x)dx 4 and | f(x)dx =7, then f(x)dx = %3D

A: Answer is below

Q: 2.Find the critical values among the given X values by: a. Correctly finding the first derivative…

A: Differentiate with respect to x we find dy/dx.

Q: 4. Compute the following: (a) e dx -1 d (Ъ) dx f'(x) dx a

A: 4.(a) The objective is to find the value of ∫-11edx

Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-8)dx…

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Q: -8 dx c – 2)(x² + 4) an upper-case "C" for the constant of integration.

A: We use partial fraction to find integral

Q: 42. a. Find df /dx if f(x) = 2 In. dt. b. Find f(0).

A: Solution is given.

Q: 16 Suppose we know that (3fx)-2)dr-6 4 and that Sxf (x²) dx =8. ise this information and properties…

A: We have to find ∫04fxdx

Q: '5 If f(x) dx = 8 and f(x) dx = 5.3, find f(x) dx. If f(x) dx = 31 and g(x) dx = 14, find [4f(x) +…

A: 1. ∫17f(x)dx=8 and ∫57f(x)dx=5.32.∫07f(x)dx=31 and ∫07g(x)dx=14

Q: In the following the symbol for the first derivative is dy/dx or Y’ and the symbol for the second…

A: Minimum value and maximum value of the function y=f(x) means On putting the value of x the value of…

Q: 7. Find for x2 + y² = y dx 2x а. 1-2у 2x b. 2у-1 с. 1-y d. y-1 e. None of the above

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