1. f (x) %3D Зx? + 2х 5 3 5 X- х- 2f (x) = 2 х+ 4

Q: (d) (x– 2)* + (y-9)* =1 (e) x² + y² = 1 (f) x² +(y+5)° = = 25

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Q: 1.What is the third derivative of y = 2x5 – 2x4 + 5x3 + 6? 2x – 2x + 5x? 40a O A. " = - O B. " 24x +…

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Q: Solve the initial value problem : f'(x)= x" – 4x³ + 12x + 18 and f(0) = 6.

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Q: Find f(x) by solving the initial value problem. X+1 f'(x) = f(1) = 8 11 #

A: Initial value problem is solved.

Q: Find f(x) by solving the initial value problem. f' (x) = 4+ 5x + f(1) = 5 · e + 10

A: Given : f'x = 4 + 5x + 5xf1 = 5·e + 10

Q: 7) Suppose y varies directly with x. If y=2 when x = – - what is y when 2 X--0.3?

A: Given the data :

Q: Find f(x) by solving the initial value problem. 5 f'(x) = 2x + 5ex + —; X f(x) = f(1) = 6 + 5e

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Q: O ) -. x- -2 46. f(z) = 1/x. - -2 fe) = V3r + 1, x=0

A: Given: 44.  f(x)=x2,  x=−246.  f(x)=1x,  x=−248.  f(x)=3x+1,  x=0

Q: 2s +10s F(s)=D (s²–2s +5)(s+1)

A: As per our guidelines we are supposed to answer only 1st one. Please repost 2nd question. Thank you…

Q: Solve the initial value problem: f'(x)=5x^28 -6x^5+12x+12and f(0) = 6

A: We have to solve the initial value problem  f'(x) = 5x28 - 6x5 + 12x + 12  f(0)= 6  Integrate both…

Q: Find the function f(x) described by the given initial value problem. f"(x) = 0, f'(-3) = -5, f(-3) =…

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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: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: 9-y" - 2y +2y=e; y(0) = 0, y(0) = 1

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Q: [d] If xz = yz and z - 0 then x = y

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Q: -12 XY and y=-S whenxe4

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Q: 8 2 f(x)dx -43, then | f(t)dt = If 8.

A: Given By the property of definite integral, we have

Q: Find f(x) by solving the initial-value problem: f' (x) = 3ex + 2x2;  f(0) = 5

A: The derivative of the function, fx: f'x=3ex+2x2; f0=5.

Q: (d) F(s) = - 1- e-s s2 +s - 2 (е) F(s) - s3 – 3s + 2

A: (-2 δ(t) + δ'(t) + δ''(t))/(s^3 - 3 s + 2) = (-2 δ(t))/(s^3 - 3 s + 2) + (δ'(t))/(s^3 - 3 s + 2) +…

Q: х4—х2+1 - [3] S [3] s e*ve*-1dx еx+3

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Q: Find f by solving the initial-value problem. f '(x) = 6x2 + 8x − 9; f(2) = 4 f(x) =

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Q: Find f(x) by solving the initial-value problem: f'(x) = 3e2 +2x2; f(0) = 5

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Q: Find the function f(x) by solving the initial value problem. f'(x) = ex - 2x ;   f(0) = 2

A: Given : f'x = ex-2xf0 = 2

Q: -x-3 F(x) = S (5t + 2) dt

A: According to question given thatF(x)=∫x3x-35t+2 dt

Q: X f(x) =< Q 14/15 7 x + 1 3 ;0≤x≤2 ;2≤ x ≤3 5 Tov Then what is the result of 3 (fx) dx 1

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Q: If y=x* - 5x² + 2x – 3 then equals dx A x* - 5x² + 2 В 4x – 10x+ 2x – 34 4x - 10x+ 2x D 4x - 10x+ 2…

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Q: [3 Marks] B1(b): Solve the initial value problem: f'(x) = x10 + 12x + 15 and f(0) = 7.

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Q: Find f ( x) by solving the initial value problem. f'(x)=e^(x)-4x;f(0)=3

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Q: S₂ (1-t) ² dt 2

A: Solution

Q: solving

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Q: 2: Find the general solution of ODE: x*y(3). 3x²y(2)+ 6xy(1)-6y= x*. Inx

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Q: find the (a) domain and (b) range

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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)*…

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

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Q: Find f by solving the initial-value problem. f'(x)=6/(x)1/2 , f(1)=19

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Q: 2y''' - 3y'' - 3y' +2y =(e^x + e^-x)^2

A: We have to solve the differential equation  For which we first solve the homogeneous equation and…

Q: Find the function f(x) described by the given initial value problem.   f"(x)=0,  f'(-5)=-5,  f(-5)=2…

A: to determine.

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

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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…

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Q: •7 49–x² r83–x²-y² x dz dy dx %D 0, -15+x²+y²

A: I am attaching image so that you understand each and every step.

Q: 8 If f(x) dx = 37 and g(x) dx = 12, find %3D [2f(x) + 4g(x)] dx.

A: Given ∫08f(x)dx=37 and ∫08g(x)dx=12We have to find ∫08(2f(x)+4g(x))dx

Q: dy Ify드a2-4x-의. then. dx x2 2x-2) 2-4x-5 einz2-4x-5)- In(z+2)]. x2-4x-5 x2 x2-4x-5 x 2 x 2 2-4x-5…

A: Consider the given equation:

Q: f(x) = é ーx46x? J6-6x -6 A) e-+6z² (-6x³ + 12x) + 2/6 – 6x Calculate f (x) 1 2/6 – 6x B) e-+6z°…

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Q: minimize F=x^2+y^2 subject to xy^2=16.

A: Let F=x2+y2 and G=xy2-16=0...(1) Let λ be the Lagrange's multiplier. Then Fx=λGx and Fy=λGy⇒2x=λy2…

Q: D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3…

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Q: Find the derivatives of the given functions. (Part D and E)

A: d)  We will need the quotient rule. For that assume u and v and find u' and v'