1 F(s) = ;L-1{F(s)} =? (s+1)(s²+1) elect the correctresponse: o f(t) = -e-t +te-t+e* %3D NONE OF THESE

Q: Vx + 3 Given f(x) then f-(x) will be %3D 4 A. 16x? + 24x +9 B. (4x + 3)2 C. (4x - 3)2 D. 16x2 – 9…

A: The given function is

Q: Let f(x) = 5x² - 4 to find the following value. f(t+1) f(t+1)= 5t+10t+1

A: Given f(x)= 5x2-4

Q: dx J (x² + 2x – 10)²

A:

Q: x² + x – 2 ? What is the point of discontinuity of

A: here is we see that function is not define when x=2

Q: x + 4 if f = 2r3 +1, find f(1). 5x – 4 -

A: Given,

Q: Determine L-1{F} if -3s2 + 20s – 25 F(s) (8 – 3)(s² – 2s + 5)'

A:

Q: When f(x) = 8a? – x – 3, evaluate f( – 4) f( – 4) =

A:

Q: 4x +3 Q10: Let f(x)= x+2 Show that f(x) is 1-1 function. Find D,, R,, and f(x).

A:

Q: x2 + (12 – 5x) | a. Evaluate f(6) given that f(x) = 8x f(6) = Preview b. Evaluate g(x + 2) given…

A:

Q: av2 (x³ – 2)(2a? – x²)2 dx

A:

Q: 7x 9. For the given functions, f and g, find (fog)(x) : f(x) = 7x²+4; g(x)=3x+2

A: To find the composite function

Q: Q Find the domain of y 1- Vx + V+ 3x-x – 3

A:

Q: V5 – 1 Given x = find x4 + x3 +2x – 1. 2.

A: Given, x= (√5 -1)/2 = (2.236067977-1)/2 x= 0.618033988

Q: 2x+4x Determine the asymptote of f(x)

A:

Q: 2 J1 4 30x(x - 1)¹dx is

A: given integration

Q: (t-3)√6t-t² dt

A: To evaluate the given integral.

Q: Put the function Q= (t-2)(t+2) - (t+4)(t-1) in the form Q= it and state the value of k

A:

Q: Find f(t). + 8s + 17 f(t)

A: To find Laplace inverse transform.  We'll use the following

Q: Suppose f(x) = - 3x+5x + 6. Compute the following: %3D a) f( – 4) + f(2) = b) f( – 4) – f(2) =

A:

Q: 56. f(x) 16x (4x2 - V16r* + 1 V16r + 1) %3D

A: 56. Here the given function  fx=16x24x2-16x4+1 Simplify the given function as…

Q: If f(x) = x² – 5 and g(x) = 6x, then g(f(x)) is equal to %3D A 6x³ – 30x © 36x? – 5 6x² – 30 D x2 +…

A: Given:     To determine:

Q: For f (x) = x² + 2x – 2, what value of g (x) gives (f– g) (3) = 11? O a) 2 O b) -11 O c) -2 d) 11

A:

Q: Find the domain. f(x): V9 – x2

A: Here, We need to find the domain of the given function.

Q: Jx-6dx is 3(x-6)% -+c 2 Ob. (x-6) +c O . (x-6)% 2 O d. 2(x-6)% -+c 3

A: I=∫x-6 dx   Let x-6=t⇒d(x-6)=dt⇒dx=dt

Q: Given f(x) —D бх + 2, find f(x + 3). О а. f (x + 3) %3D бх? + 20х + 6 O Б.f(x + 3) %3х+5 О с. f (x +…

A:

Q: (D3 – D)y = -2(1+x) + 4e* – 6e¬* + 96e3*

A:

Q: Let f(x) = 3x – 1, and g(x) = 64x3 – 27. Find (fog)(x). a. 192x3 – 28…

A:

Q: Let f(x) = x² + 7. Find and simplify: f(x + 6) - f(x) O 12x + 50 O 12x + 36 O 12x O 50 0 36 O 6x +…

A: We can simplify and find the correct answer in the below steps.

Q: (x + 2)³ y = (x² – 4) ||

A: a2-b2 =(a-b)(a+b)

Q: Let f(x) = 2x – 5 and g(x) = x² – 7x + 2. Then (f o g)(x) = (go f)(x)

A:

Q: x² + (13 – 3x) a. Evaluate f(5) given that f(x) : 8x f(5) = Preview b. Evaluate g(x + 2) given that…

A:

Q: xy – 3y + 3x² – 9x =

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.