Exercises: • In problems 1-2, show that the function f is continuous at the given point. Re(z) 1.f(z) = - 2z2; zo = ein/4 %3D Z+iz z3-1 2. f(z) = } z-1 3, Izl + 1 ; zo = 1 Iz| = 1

Q: 10. (8x)" W 39xt (21x -12) mWX = mYW = mYX = (10x + 9) MVXW = Gina Won (A Things Aigebra, uC,…

A:

Q: If F(x) = f(g(x)), f(2) = 8, f'(2) = 4, g(5) = 2 and g' (5) = –2, then F' (5) is %3D %3D 16 -8 12

A:

Q: 11. f(x) = 2(x – 1)² %3D | f(x) -1 1 2 3

A:

Q: If f(2) = 1, f'(2) = 2, g(2) = 2 and g' (2) = 1, then f(x) g(z) %3D %3D %3D

A: Given : f2=1f'2=2g2=2g'2=1

Q: 19. Suppose g is a differentiable function for all real numbers. Given that g(x) dx = 12 and (g(x)…

A: To find: The value of ∫47gx+5dx. Given: The differential function g is ∫27gxdx=12 and ∫24gx+3dx=7.…

Q: Explain why, no matter how the circuit is completed, Pip must place an even number of additional…

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Q: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

A:

Q: 5. Which is the inverse of f(x) =2? %3D Or (2) = H 241 Of (x) = 1- Of (x) = 1 1-c f(x) = 1+a

A: To find f-1(x) We interchange x and y and solve for y as function of x

Q: f f(x)=- X+1 2x+1 1 = (2x + 1)²* 1 (2x + 1)² O 3x+1 (2x+1)²* 3x+1 O (2x + 1)² then f'(x) =

A: Topic: derivatives

Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

Q: 7. If f(x)=√(1-1²)et² dt, on which interval is f decreasing?

A:

Q: S(2) dx = 6, / f(2) dx = 3, f (x) dx = 3, f(x) dr = 7 Let -10 -10 -6 | f(x) dx Find J-8 8- and .…

A:

Q: 14. Given the functions f(x)=x +1, g(x)=/2x and h(x)=- x+3 find: %3D a) f(8(9)) b) f(8(x)) c)…

A: Given  f(x) , g(x) and h(x)

Q: ax? If f(x) = if x > 1 then the bæ + 2 if a<1 values of a and b such that f is differentiable on…

A: For function to be continuous

Q: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: If f (2) = 322 + 4 and f(1) = 7, find f(z). f(z) = -r' + 4x + 4 f(r) =-3r2 + 4z +6 f(z) 3x + 4x f(z)…

A: The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And ∫afxdx=a·∫fxdx Given: f'x=3x2+4 and f1=7

Q: 8. f(x) = 3x - 1 f(x) = f(1) x - 1

A: The objective is to solve the above expression.

Q: 5. f() = {x? - 4 U x* -3 Evaluate f(4), f(0), f(-3) and f(-2/3) }" -2 if x = -3'

A: The objective is to evaluate f(4), f(0), f(-3) and f(-2/3).

Q: 1. y = 4* y = 1. • 3* %3D 3. f(x) = 3*+ 1

A:

Q: Suppose that f(x) r'(x) = 4²x+5]n(4) - s+2 + 5x Find f'(x). #

A:

Q: 3. f(x) = x² – 5x + 9 4. f(x) = 1/x² %3D

A: we have to find range and domain

Q: 2. f(x) f(0) S() 0 f(0) f x) 0I=

A: First we  find equation of line that is  y= mx+b Here m=-2 and b = 2 So equation form and it is y=…

Q: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

Q: If f(x) = then f"(x) = = X √ ² ( 2³ + (t³ + 4t² + 5) dt 0 ←

A: Let,Using integration formula So,If  dtPut , dt = F(t)Then So,

Q: Find the following using the table below. 3 4 f(r) f (x) g(x) 4 4 4 3 4 (x),6 h'(2) if h(x) f(x) ·…

A: It is given that h(x)=f(x)⋅ g(x), h(x)=f(x)g(x), h(x)=f(g(x)) We have to find h'(2).

Q: 40. YA 3 2. 0 y = f(x) 2 +3

A:

Q: If f(x) = (2² + 5x + 3)“, then s'(#) - [ f'(x) -

A: To find the derivative of the given function, we need to use chain rule of differentiation and some…

Q: 2x-3 5. Let f(x) = find as Ax - 0 Ax 3x+4'

A: Given that: f(x)=2x-33x+4

Q: 2 If f(x) = (x³ +3x)“, what is f'(æ)? O f'(x) = (x³ + 3x) O f (x) = (x³ + 3æ) (3a² + 3) O f'(x) = 2…

A: Follow the steps.

Q: [*[f(x) + g(x)] a 6 -5 f -2 Y = 7 -3 7 x -6 9 -2 Y 10 5 3 5 2 x

A: We have to find the value of given integration.

Q: What is the value of In[f'(2)]if f (x) = e*?

A: Our Aim is to tell the value of ln f'(2) if f(x)=ex-(i)

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.