1 10x Evaluate f dz S dx e dy. (10e-10)/3 10e/3 10/3 10e-10 10

Q: 14 نقطة Q) Find dy/dx of the following * :equation (x² +x)(x' - x +1) y: dy/dx = -3/x^4 O %3D dy/dx…

A: Given y = x2+xx2-x+1x3y = x4-x3+x2+x3-x2+xx3y = x4+xx3y= x+1x2

Q: en 0 3 | f(x)dx=0 and. -1 S 11 11 5 55 6 f(x) dx = = 11 6 , evaluate 1 J 3f(x)dx - [2f(x)dx.

A: We will distribute the integral in two parts .

Q: Solve the problem. Suppose that " g(t) dt = 4. Find S* ste) dx and *- gt) dt . -1 1; 4 0; 4 O 1; -4…

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Q: 10. Evaluate: +4x dx (a) (b) (x2 -2x 4) dx (c) (t2-t) dt (et cos t) dt (d) dx

A: Here, we use the formula that integration of x^n is x^(n+1)/(n+1) as shown on board.

Q: 1. IT (2, 4) dar dy =/| f(x, y) dy dx %D 0. 0.

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Q: 4) xy dx + (y + 1)e¬*dy = 0 Ans: (x – 1)e* =-+ + c (Xie, 2010)

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 1 1 10z Evaluate f dz f dx f e dy.

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Q: 18 12 | f(2)dz – f(2)de = f(x)dx | f(x)dx 4 where a = and b =

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

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Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

Q: 12 d*x(t) 5 dt3 d²x(t) dt² + 5x(t) = 3cos(2t) d²x(0) 2, dt2 dx(0) 1, dt x(0) = 1 3s2 + 5s + 1 X(s) :…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: dy 1. Find general solution for =x²y° +2y +x° +2. dx

A: Dear learner,  As per our guidelines we can provide the solution for first one only. Kindly post…

Q: 5. Find the dy of the followings: dx (i) y = x²lnx (ii) y = (iii) y = (4x² – 20)(6x +5) (iv) y =…

A: dxndx = n.xn-1. Chain Rule of differentiation : If f(x) and g(x) are two differentiable function…

Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: 18. If x? – xy + y? = 3 find y" (second derivative) %3D 18 12 12 18 В. (x – 2y) C. (x – 2y)² A. D.…

A: Given:- x2 -xy +y2=3 To find:- y''

Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

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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: SOLVE BERNOULLI´S ODE y1/2 (dy/dx)+ y3/2 =1 ;   y(0)=4

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

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Q: 4. If ( Inx dx = f(x)[In(x) + 1] + C, then f(1) = A 1 B D -1

A: Solution

Q: (e + 1)²e-Ydx + (e* + 1)³e¬*dy = 0

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Q: dy 1 andy 3x? + 1 if- dx Find- atx = -1. dt dt 1 6 -6 ||

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Q: (a) a) ₁₁ (x² +y) dy dx. Show all your work! 2 (b) ***1 1 dy dx. Show all your work! 0 2 ¹y² ff 1 dx…

A: SOLUTION-

Q: 1. Find the dy of the followings: dx (iii) y = (4x² – 20)(6x + 5) (iv) y = (4x² – 20x + 50)6

A: For given (3) and (4) , we have to differentiate it with respect to x

Q: dx = 6, find dt dy Ify = 2x3 + 6x and whenx = 4. dt wwww A 582 782 None of these D 822 E 732

A: Using derivatives.

Q: 17. If y = x, then dy/dx (a) x²-² (b) x²-1 lnx (c) x²²(1-In² x) (d) x²-²(1–In x) (e) None of these

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Q: dy 6. Determine for dx In( xy) + x² – xy 2 -1 e +1

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Q: 3. f Arctany dy 4. fx(2x - 1)'dx 5. fycsc²ycoty dy 6. fxsin4xcos4x dx

A: The given integrals are;  5) y csc2y coty 6) x sin4x cos4x.

Q: II. Find dy/dx of the following functions: 1. y = cosh √√4x²+3 2. y= sec hx² x² +1 3. y=xcsche4x

A: See this solution in below

Q: d g(r)= 3re³ %3D e y= e² – e-z 5 f. 8- 3+ el

A:

Q: 1. Find the dy of the followings: dx e* (i) y = x²lnx (ii) y = Inx (iii) y = (4x² – 20)(6x + 5) (iv)…

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Q: if : 1 1 + + 1+x² ' 1+x° 1 t...+Tx" 1 f(x)=1 1+x a+1 a+1 and / f(x)dx=2 then find : / f()dx = ?

A: using the given value of the function and definite integral we need to evaluate the unknown value of…

Q: сох3х S* (1/4 – 1) dt dx J3

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Q: (хе* + 4e* + 4eУ + 4lny) dx + ( хеУ + — dy %3D0;B у (0) — 0

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Q: Q5. Evaluate ſ^₂ ¹¹ xy dx dy. ry+1 y²

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Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

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Q: 2r –1 15. Evaluate dx. (x– 2)(x+1)' A) hx- 2| + hịx + 1| +C C) -hx – 2| + Inx + 1|+C B) hx- 2| – hịx…

A: To evaluate: ∫2x-1(x-2)(x+1)dx

Q: 4. ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e

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Q: S 1 dx = (x - 1) Vx Select one: O a. а. 6x- 3ln x +1 6, х —1 O b. Vx + In Vx +1 X, × -1| O C. 6x…

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Q: 1. fx³e*/2dx /4 2. S*x sin 2x dx

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Q: Given f(1) = 1, f(1) = 5. g(1)= 3. g'(1) = 4, f'(3) = 2, and g'(3) = 6, compute the following…

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Q: 1 Q22. If y=tan' x+ tan dy - then -is: dx (d) T 2 (a) 0 (b) 1 (9 (p) 1+x

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Q: 1 1 Evaluate f dz[ dx [ e dy. бе/3 (бе-б)/3 О бе-6 6/3

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Q: 1 1 Evaluate f dz dx f ez dy.

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Q: dy 2. Find the general solution to the ODE dx 3x %3D x + 1

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

A: Solution is given.

Q: 3Solve the 0.D-E. below given yat + (fy}+t)dy= 0

A: We have to solve given problem:

Q: 6. - ydx + (x ++ Jy )dy = 0 7. (1+x*)dy + x(1+ 4y°)dx =0 8. (e* + y)dx + ( 2+ x+ ye" )dy =0 2y 9. 4.…

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Q: 0 1 Q3:Evaluate the irtegals [(x+ y+1)dxdy -1-1

A: The detailed solution is as follows below:

Q: 4. If x = 1+1 & y==1-t² then dy - at t =1 is dx а) 1 b) 2 c) -1 d) - 2

A: Value of dy/dx at t=1 is

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: