If f(x) =sin(x) then the Taylor's estimate R2(x) = .A sin(3) 6 .B _cos(?) X- .C cos(7) .D cos (3) 3.

Q: 9. Find f' (x) for the function f (x) = sin? (cos(4x)) 10. Find f'(x) for the following functions:…

A: Given:          f(x) =sin2cos4x first derivative        ddxfx =f'x      f'x=ddxsin2cos4x    Applying…

Q: 1. 2. (√ex + (ex)³) dx /22sinx cos x dx

A:

Q: Differentiate the function. 8 + sin(t) f(t) cos(t) (a) f'(t) = Find f'(T). (b) f'(1) =

A: a:Here, f(t) =(8+sin(t))/cos(t)The derivative of f(t) is calculated as follows:

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: S COS X sin x+sin³ x dx. (b) ſ sec²x tan x+4tan³ x dx.

A:

Q: V3 sin- (x) dx V1 – x² 0.

A: Here we have to find the given definite integral value.

Q: 3. For y = 3 sin x + 21, the third order derivative (a) -3 cos z +21 (b) -3 cos r 4. For y = e-2-50,…

A:

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

A:

Q: Let h(x) = tan(2x + 2). Then h'(2) is and h''(2) is

A: The given function is: h(x)=tan(2x+2)

Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: ilf find f'(x). Answer f(x) = 3 sin x 1 + cos a

A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Find L {f(t)} if f(t) = cos 5t + sin 2t

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 4 (a² - y²)² 4. g(x) = (3x² + 4x - 5)5 3. 2 =

A:

Q: 1 sin(x) (D²+1)³

A:

Q: If f(x) = sin(r*), find f'(x). 3z° cos(=") CoS Find f'(2). 3a cos(r³)

A:

Q: f(x.y) = xtan(). =tan( ес

A:

Q: 2x sin-1(x²)dx =

A: This question is taken from the indefinite integral in which we have to choose the correct option…

Q: Find the value of f(0) when 3 sin(2t), f( f'(t) 1. f(0) 2. f (0) 3. f (0) 4. f(0) 5. f(0) = = = = =…

A:

Q: -1 Let f(x) = tan-¹ e²². Find f" (x).

A: The solution is given below

Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: (x² +8) cotx 2 - cos x csc x Find f' (x) when f (x) = 2x cot x – (x² + 8) csc²x A. f' (x) = csc²x 4x…

A: As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Product rule: f·g'=f'·g+f·g' The…

Q: Find f'(z) if f(z) = 8 cos(z) + 9 sin(z). Answer

A:

Q: 4. Find the derivative of the functions. (2x2-3) a. y = (x247)5 sin x b. y = 1+cosx

A:

Q: Let h(x) = tan(2x + 8). Then h'(3) is and h''(3) is

A: This question is about application of derivative

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.