3- 2+ -4 -3 -2 -1 -1 1/ 2 3 4 x -2- -3 . Figure 1: y = f(x) 4. 1.

Q: -16 1Δίνεται η συνάρτηση f)- 2x+8x i) Ποιο είναι το πεδίο ορισμού της f i) Να απλοποιήσετε τον τύπο…

A:

Q: +2メ+2 2=f(x.y)-4xy 3. +2メ+2y2= T %3=

A: Derivative: - The function's derivative is the equation we discovered. The derivative is defined as…

Q: -y3_1 If f(x, y) #1 %3D I-1 3 ,x = 1 then fy(1,0) – 3fz(1,0) =

A: lim (x,y)→(1-,0) f(x, y) = lim (x,y)→(1+,0) f(x, y) = ∞  f(1, 0) = 3   The function is not…

Q: 1-х 26. f(x) =- х+2 27. /(х)- Vx* - 3

A:

Q: In Exercises 7–10, use the formal definition of limit to prove that the function is continuous at c.

A:

Q: 10. (x, y) = x² +xy – 2y – 2x +1 %3D - 2 16. f(x, y) = xy+ - + 4

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Q: f (x+h)–f(x) ,h+ 0 h fx) = -10x + 3h - 12h f(x) = 6xh + 3h - 5h O ) = 6x • 3h -5 fx) = 6x + 3h + 5

A: Let's find.

Q: Derivatives of quotients Find the derivative of the followingfunctions.

A: "Since, you have posted a question with multiple subparts, we will solve the first three subparts…

Q: 2 > x>1 4 2x > 2 52x>4 62x>5 (4 x + 2 b) f(x) = 16 x² + b 1)is the above function continues at x=2.…

A: We use the definition of continuity at a point to solve the given question, i.e., A function f(x) is…

Q: 2 The derivative of y = 3x? 3 + 3x is 2x 3 A. y =** 2 2 3 x° + x´ +3 3 4 4 В. у B. y' = +3 2x2 + 3x…

A: Derivative.

Q: -2 3 A = :), f(x) = -4x + 2 5 3 ON(-20 10 -12 -10 0 3 OB ( ) 8. -10 -12) -18 35

A: Here we will find f(A),

Q: y''-3y'+2y=5e^3x,y1=e^x

A: Reduction of order is a very significant and basic method to solve higher-order linear differential…

Q: 11. In the function y = 3x2 - 3, y is replaced by y and then y is replaced with y +2 ; the new…

A: Given:     Function y=3x2-3   Here y is replaced by 12y       substitute y=12y      12y=3x2-3…

Q: if f(x)={ -3x       for x -1  find f(-2)  a. -6 b.9 c.6  d.-1 e.0

A:

Q: Obtain the general solution. Use homogenous functions for this problem. (2x°y – xy² + y³)dx - (2x³ -…

A: on solving this equation we will convert ist in homogeneous function form that is y/x form than we…

Q: 4. s=+- 5. y= X+1 2 x+ 1 6. f( x)=. 1- 2 x 2 7. y=2 x + 3 x'

A:

Q: 59. (а) у 3 f(x) + 1 (b) у -- fo) - 1 (e) y = 25) y =f(x) (-1, 2) (0,0) (-2, 0) (2, 0) Ia.-2)

A:

Q: 7. (a) f(x) < 0 X= -1 X = 1 (b) f(x) 2 0 41 y. 3 y = 0 -3 3- -3

A: Graph of the function is given we have to finda) f(x)&lt;0b) f(x)≥0

Q: 5. f(x)=2(x- 2)*– 1 10 4 46 810 -10-8-6 -4-2 -2- -4 6, CO

A:

Q: dž 3 9. with x(0) = dt -1 -3 x1(t) = help (formulas) x2(t) : help (formulas)

A:

Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: Find the function y(x) satisfying -8/9 = 6x dx and y(-1) = - 4. dy :-8/9 The function y(x)…

A: Integrate the equation dydx=6x-8/9 with respect to x.…

Q: X - X (x -x* Y (r-F)} (x-X{r-F) Y-F 2 4 3 6. 6. Compute: X = Y = E(X-XXY-Y)- N-1 B A = Y - B*X = 2.…

A: The table is given as follows x (x-xbar) (x-xbar)^2 y (y-ybar) (y-ybar)^2 (x-xbar)*(y-ybar) 0…

Q: f(x) = x* + 3x2 - 6 avenge Spe : fro-fa) [0,5] f(s) = 5":5-25-6 : 694 694+6 760 %3D 140 %3D b-a 5-0…

A: on using Newton rephson method we can solve this equation

Q: -2 27. The first derivative of y = is (4x+1)3 а. -24 b. 24 C. -6 d. (4x + 1)* (4x + 1)* (4x + 1)*…

A:

Q: 2) f(x) =15 - 8x A) s'(s) = B) s"(x) = x 2 C) 3x- 15 s"(x) = 8. D) s (x) = x - 5 3.

A:

Q: 4y" + 2y' + 5y = e=t y(0) = –1 y'(0) = 0

A:

Q: 1°- 4+ 4r2 -4 dr Co T. (1²-1)(r²+2r+2)

A: Indefinite integration is the backward process of differentiation. Through integration, we find a…

Q: 3. f(x) = (3x – 2)* %3D 4. f(x) = (x² + 1)° (xr? – 1)² | (2x – 6)* f(x) = (x + 7)7 5. -2 6. f(x) =…

A: See the details solution in below

Q: -2r +1 s2 2) f(x) = 5r-11 2 f(2) = f(-4) = f(8) = X

A: Given,

Q: 4. F(x)- F(x)=L x-1 5. Gx)-8-2x 6. h(t)= 2-1

A: For a real valued function f(x) We have to find all points x where f(x) is well defined Those points…

Q: -5 f(x) dx = 6, | f(x) dæ = 6, f(x) dx Let = 2. -2 /" f(2) dz = Then -5 (6f(x) – 6) dæ = and - -2

A:

Q: (2x +1 if x<1 F(x)=1-2x +3 if x21 2. f(-2) = f(6) = f(1) =

A: Here we have to find the value of the given function at the required points. Initially we have to…

Q: :- (t3 + 5t2 + 7)dt If f(x) : then f'"(x) =

A:

Q: 1. f(x)= 4x – 3 2. F(x) = /1+x 3. G(x)=|1 – 2x| 4. h(x) - х* +3 х?- 2х +1 5. f(x)= X-1

A: We have to find domain and range of given functions.

Q: If x = xf(y)- 1 then, 1-f(y) 1. y - 1-f) xf') 2. y = L)-1 xf G) 3. y--fo) 4. y =-f)

A: Given x=xfy−1 Use formula  ddxxn=nxn−1 and ddxc=0, where c is a constant. Differentiate  x=xfy−1…

Q: -8 f(1) – 4 g(4) =[ %3D 8- 6+ y= f(x) 2+ -8 -6-4 6. -4+ y=g(x) -6+ -8- ఈ

A: Given, The graph of the functions  y=fx   and  y=gx We have to find the value of expression…

Q: 1) f(x,y)= 2x² – 3y – 4 2) f(x, y) = (x² – 1)Xy + 2)

A: Solution :-

Q: 21. g(x) = 2x* - 20x + 18 22. f(x) = 3x* - 15x + 12 23. F(x) = Vx – 1 25. f(x) = 1 -/3 -8 27. G(x) x…

A: Given that: g(x) = 2x4 -20x2 +18. And G(x) = -8/(x2 + 1) We find relative extrema of both function.…

Q: f(x) = -0.1x4 - 0.15x3 - 0.5x2 - 0.25x + 1.2 at x = 0.5 using: first backward difference with…

A: f(x) = -0.1x4 - 0.15x3 - 0.5x2 - 0.25x + 1.2at x = 0.5 using: first backward difference with…

Q: g) t(t-5)². i) (x-1) (x-2)(x-3). h) x (x²-4)². j) (y-6) (y-4) (y + 1).

A:

Q: a) | f(x)dx = -10 %3D 4 b) f(x) dx = -10.5 4 c) f(x) dx = -17.5 10 d) / f(x) dx = 9 %3D 10 e) -5…

A:

Q: 1 + X f[X_, Y_] := 2y-1-를x (1+ ) (y-1)2 (1+ 2) (y - 1)2

A: Given fx,y=1+x2y-1-131+1xy-12

Q: 5. Obtain the general solution. Use homogenous functions for this problem. (2x°y - xy? + y³)d« -…

A: We will solve the following

Q: 3x-1 х-1 che following equation for x: =X - 4

A: The given equation is: 3x-15=x-x-14 To solve this equation, take the "Least Common Multiple " on the…

Q: 19.yf(x) = 2|x – 1|; f(-2). f(0), f(¿). f(2), f(x + 1), f(x² + 2)

A:

Q: (b) f(z)= (4 – 5e*)³ x² + 1 (c) f(r)= ez %3D (d) f(z) = e=²–5z+4 ez-5x+4 (e) f(x)=xe² – e² = re² –…

A: We can solve this as follows: