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: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

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

A:

Q: 50 30 SO then s0 f(x)dx equals? Choose one. ()B-A (2) 2A+2B (3) 2B (4) A+B (5) A-B 16) 0 (7) 2A…

A: To evaluate the given definite integral.

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

A:

Q: 2 What is the value of f'(0) if f(x) = (x² – 2x – 1)3? %3D 4 3 Option 1 Option 2 4 2 3 3 Option 4…

A:

Q: Suppose that f(x) 2 4x Find f'(x).

A: use quotient rule for differentiation

Q: For f(x) = (2a* + 3x)(5x*), find the derivative of f(x). 80x7+ 60x3 20x7-30a3 O 10z8 + 15x4 O…

A: We will use concept of differentiation to solve this.

Q: a. J(a) Problem 9: Draw the derivative of the function -10 11 F3 -5 10 10 0 -5 -10 V F5 5 F6 10…

A: We have to draw the graph of f(x) derivative by see it's original graph f(x).

Q: 6. Let f(x) = -5x¹ and g(x) = 2x + x. If h is the function defined by h(x) = f(g(x)), which of the…

A:

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

A: To find f'(x)

Q: 8. Find f'(x) for (a) f(x)=(x² +3x+1)(2x+3) 2x-3x+1 (b) ƒ(x)= %3D

A: We need to find the derivative of the given functions. For (a),

Q: Provide an interpretation which is true and one that is false. (∃ x)(P(x,b))

A:

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

A:

Q: 1. Which of the following are one-to-one functions? (Choose all that apply.) a) f(x) = x? b) f(x) =…

A:

Q: If f(x, y) = (5x- y²) (a) f(1,4) find the following.

A:

Q: The derivative of f(a) = -a* - 4 * – 2 a2 - a is O f(a) = -4 a – 12 a - 4 a2 O f(a) = -4 a - 3 a2 -…

A: We have to find the derivative of f(x) = -x4 - 4x3 - 2x2 - x.

Q: Compuie ite : Newton's.. divided diff erence tabble and hence Com pule Ine Raicis . for. ine…

A: Let       k 0 1 2 3 4      xk 2 3 6 7 9    fxk=fk 15 39 243 375 771 The 0th divided…

Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

A:

Q: Use properties of logarithms to find the derivative of f(r) = In ((2. 2)

A:

Q: 1 (a) y= %3D - (b) f(x) = 3(r³ – e²) %3D 4 (c) h(x) = 3x³. %3D

A:

Q: If f(x) = (2x + 1) (x - 3)°, then f'(2) = %3D

A:

Q: The inverse of function f(x) = x3 + 2 is а) f-1 (y) %3 (у - 2) 1/2 b) f-1 (y) = (y – 2) 1/3 c) f-1…

A:

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: If f(x, y): = x²y (5x - y²) "I find the following.

A:

Q: Question 8 8. Given f(x) =(3x² + 4x)(x –5). Which of the following is TRUE for f'(x)? (3x° +4x)(6x +…

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.