) Let f(t)= e⁹t t6 + cos(7 t) e4t then L{f(t)} = ?

Q: a. f (x) = 4x + sin(x) - e* = 0

A: The objective of the question is to find the root of the equation f(x) = 4x + sin(x) - e = 0. This…

Q: Example #3: Consider the function fcx) = (2x+1) √√x-1 Evaluate: a) b).. (³x f'(x) dx. 5 fcx) dx 2

A:

Q: Calculus Question

A: To evaluate the integral.

Q: Let f(x)=3x3+x and g=f¯l then g'(4) = %3D .A 1/2 .B 1/10 .C 1/5 .D 1

A:

Q: If f(x) = sin x 7T find f %3D (a) 1 (b) / 2 2. . т (c) 1– 4 (d) V2 1+ (e) /2 (1- 3)

A:

Q: Suppose F(x) = | cos(2?)dz. Find F'(x).

A: We have to solve the problem

Q: T (8) If g(x) = sin(x) *cos(x) find g'(-).

A:

Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

A:

Q: 5. Evaluate (x) dx for the following functions: 1 (a) f(x) = Vx + (b) f(x) = e2x %3D (c) f(x) =…

A:

Q: If f(t) = 103t-5 x e2t, determine the value(s) of t so that f'(t) = 0.

A:

Q: If f"(x) = V - cos(x). f'(0) = 2, and f(0) = 0, find f(x). %3D

A:

Q: 3- 2 -3 2 -1 2 3 g(x) = sinh(x) -1 -2

A: the symmetry used here is the y-axis which divides the graph into 2 equal portions.  the graph given…

Q: In f(x) dx = F(x). F(x) is called the

A: follow the procedure given below.

Q: Compute f(s), where f(x) = cos oz and 8 >

A: We have to find out the Laplace transformation of f(x) = cos

Q: (2) Show that f(x) = e³x cos(2x) is of exponential order.

A:

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

A:

Q: Find F(s). F(s) = L{e-⁹t cos(2t)}

A: We have to find .

Q: 1 If f(t) cos(6t), find f'(t). Use exact values. f'(t) =

A:

Q: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

A:

Q: g(x, y) = sin (T ¤y) + log3 (x – 3y) -

A: The given function is                          gx,y=sinπxy+log3x-3y…

Q: Suppose f(2) = 1, f'(2) = –6, and | dH H(x) = (1 + f(x))³. Find dx Н (2) %3

A:

Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: 6. If /f(2)dæ = (x + 5)*eª + ln(|æl) + C, what is f(x)?

A:

Q: 15 .3 Suppose f(x) da = 2. f(x) da | f(x) da = 5. What is | f(æ) da? 3, and -8 -10 10

A:

Q: Suppose f(x) = x² In(x). then f"(e) equals

A:

Q: IfI(u) = [log, (1-2u cos x+ u' )dx, then prove that, I(u)+I(-u)-DI(u²).

A:

Q: Suppose f(x) has the following properties: f(3) 5 || f(7) 2 7 - 2x е * f(x) dæ 12 3 Evaluate: 7 I…

A:

Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2

Q: Let Find f(x)|x=7 = y = f(x) = ( 2 ) ²³ d dæ f(x)\x=7² sin x.

A:

Q: 9. Find f(35) (x) for f(x) = cos (2x)T = COS

A:

Q: f(x)=cos(x) Glx)こxや+1 d f(9(x) = t3 clx

A: We have to find derivative

Q: If f (x) = 3x + 5 and g(x) = x³,finc а. (f + g)(x) b. (f/g)(x) c. f(g(x)) с. d. (f°f)(x)

A: