5) Determine the entire function f(2) = u+ jv satisfying Re(f(2)) = u(x, y) = ae" cos(y) + r? – y², where a is equal to 2 and f(0) = a. Also compute f'(2) at z = a.

Q: Suppose that f (1) = 1, f'(2) = 5, f'(1) = 4, g(1) = 2, g'(1) = 7. Find a. (fo g)'(1) b. (9((x)))…

A:

Q: Determine whether the following series converge or diverge. n b) Σ 5n n=1

A: The given series is .We need to determine, whether the given series is convergent or divergent.We…

Q: Find f. f"(x) = cos(x), f(0) = 3, f'(0) = 6, f"(0) = 4

A:

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(7x/2) = 0 %3D %3D f(x)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: Find F' (÷) if F(x) = 2 cos-1 Vx. %3D

A: We will find the value of F'12 where Fx=2 cos-1x in the following step.

Q: Find div(V), where V= (x²+y² + z²)¯²(-3x, -3y, –3z].

A:

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: (a) Prove that the real number p3 is an irrational number. That is, prove that If r is a positive…

A:

Q: Let c =3 If f (x) : Cind f! (0

A: The function given is fx=x2-cx+1 The value of c given is 3. Substitute the value of c in the given…

Q: Find y as a function of x if y(1) = 1, y'(1) = 4. y = x²y"-7xy' + 16y=x6,

A:

Q: Find y as a function of if y(0) = 18, y'(0) = 28, y'(0) = 21. y(x) = y"-9y" + 20y = 24e,

A:

Q: Find f'(z) of f(z) = 3πi.

A: Compare the given function f(z) = 3πi. with f(z)=u(x,y)+i v(x,y) So,  u(x,y) =0 and v(x,y) = 3π

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: 2. Use the theorem in Sec. 23 to show that f'(z) and its derivative f"(z) exist everywhere, and find…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

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Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x) b) Let y=cosx-sin.x , show that…

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Q: Find y as a function of a if y(1) = 8, y'(1) = 6. y = x²y" + 3xy' - 35y = 0,

A:

Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

A:

Q: Find the function f(x), such that f(x)= In(3x) J ƒ(1)=1.

A:

Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Find f if f"(x) = 0, f(0) = 2, f'(0) = 1

A:

Q: Fihd f if f"(±) = sin(z), f(0) = -1, f'(0) = -1, f"(0) = -4. %3D f(z) =| D

A: Given: f'''(x)=sin(x),  f(0)=-1,  f'(0)=-1,  f"(0)=-4

Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

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Q: Find y as a function of if y(0) = 19, y'(0) = 19, y"(0) = 4, y"(0) = 0. y(x) = y(4) 4y" + 4y = 0,

A: y(4)−4y′′′+4y′′=0y(0)=19,y′(0)=19,y′′(0)=4,y′′′(0)=0

Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

A:

Q: Find y as a function of x if y" + 16y' = 0, y(0) = 0, y'(0) = 4, y'(0) = -32. y(x) =

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.