COS x Compute r4 + x2 + 1 8.

Q: Q5) Find fs) if you know that g(x) cos(x- 1). fx) = 3tan(x) at r2

A:

Q: Find f' (x) where f(x) = -5x² - 2 cos (x).

A: fx=-5x2-2cosxUsing  differentiation formuladdxxn=n .xn-1ddxcosx=-sinx

Q: sin(2x) Compute fonda. x(x²+4)

A:

Q: sin, ifx T 2л

A:

Q: Q: Find fo 1- y = tan/2/2x + 7 (x² +x)(x² -x+1) 2- y = x*

A:

Q: Find f(x).

A: Given,

Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

A: Use the given information.

Q: 2x + 5 What is true about the function Ax) = X+3 as x → co?

A:

Q: A 61. f(x) = -2 cos (3x); 0 sxs 1/3

A:

Q: Evaluate f 1+cos 4x dx 1-cos 4x

A: To evaluate the given integral.

Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

A:

Q: 2Cos3xSenx +Sen2x Simplificar: E= %3D 2Cos7xCos3x- Cos10x

A: Given E=2cos3xsinx+sin2x2cos7xcos3x-cos10x To simplify this the identities used are…

Q: cos kT + k2 2k k=4 IM:

A:

Q: 18. f (x) = x3 − cos x

A: f(x) = x3−cos(x)d f(x)dx=ddxx3−cos(x)            =ddx(x3)+ddx(-cos x)            =3x2-ddx(cos x)

Q: r 3n 4 Evaluate sin'x · cos'x dx 5. n /2

A:

Q: 4 cos x h(x) Vx+2

A:

Q: Let f(r) = cos(4r + 4). f'(x) =-4 sin(4r -4) f'(2) = | 0

A: Solve the given problem.

Q: Find f'(x) given f(x) = cos*(3x). %3D

A:

Q: 1. f(x) = 4x³ · cos x

A:

Q: Solve for x: 3sin x + /2 cos x: V39 0 < x < 27.

A:

Q: Find if f(x, y) = x2 +2xy cos x .

A:

Q: The complementary function of (D² +4) y = 3 cos2x is О CF %3D Сј cos(-2x) + C2 sin(—2х) O CF = C1…

A: We need to find the complementary function . We have the function , D2+4y=3cos(2x)  Writing it in…

Q: 2 V9 - f(x) = for -3 <x <0 TTX -x +3 coS for 0 < x < 4

A:

Q: Find f'(x) where f(x) = -5x2-2 cos (r). %3D

A: The given function is fx=-5x2-2cosx.

Q: b. f(x) = -3 cos [4 (x -+ 2

A: Givenf(x)=-3cos[4(x-π8)]+2.

Q: Evaluate D3(sinx – 4e) A cos x-32 ex B -cos x-32 e?x -sin x-32 ex sin x-32 e2x

A:

Q: 1 x³ y =e*(dsin²3x-tanx ) - 10 y'=? (fх +1)

A:

Q: 3. Derive the reductive formula for f sec" (x) dx.

A:

Q: Differentiate. f(x) = 5x° – 6 cos(x) %D f '(x) %D

A:

Q: 1. f(x) = cos (-:-)

A: From graph, it is clearlimx→∞cos1x =limx→-∞cos1x = 1

Q: d 5s- Cos-3 s(s*- 1st1)

A: We use partial fraction method to decompose given function of s and then use inverse Laplace…

Q: сп/2 Cos 2x d.x 11 Jo

A: V

Q: f(x) = (cos x – 3)* + 2x?

A:

Q: f(x) =- cos on the interval -360° sx<360°

A:

Q: 2. Find g'(x) for g(x) = x cos-l-V1- r²+ez³ cos z. [Simplify answer as much as possible.]

A: topic -derivative

Q: Determine f,(x); f(x) = cos(2x³ +n²)

A:

Q: CoS X F 2x 7x

A:

Q: If f(x) = 6 sinx + 6 cos a, then %3D f'(x) = %3D f'(4) = %3D

A: Simply take the derivative using standard derivative forms.

Q: F(x) = x tan-1x – In v1+x2

A:

Q: Q5) Find f((s) if you know that g(x) = cos(x² – 1). S(x) = 3tan(x*) at vr?

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: 4. Find f'(x) if f(x)= In (2x) + cos (6x)

A: Given- f(x)=ln(2x)+cos(6x) To find - f'(x) Here we will use the following formulas-…

Q: Q3/ Find ∫ √x * Sin2 (x3/2-1) dx=? (by substitution)

A:

Q: 1 x³ -1 y =e*(dsin 3x- tanx')+- 10 y' = ? (fx +1)

A:

Q: Suppose f(x) =sin(3x- 2). Evaluate: A -3cos(3x- 2) +C B ® --cos( 3x – 2) +C © ;cos(3x – 2) + C D D…

A: Topic = Integration Correct option = B

Q: find for f(x) =|x| . [-x , a] - IT - .a 0.b0 T.cO 2n.dO

A: We have to solve given problem:

Q: cos2x – sin2x cos2x F(x) +C. What is F(M)? For dx%3D cosx – sinx 3

A: A detailed solution is given below

Q: )Evaluatef 4x cos(2-3x) dx

A:

Q: P21 601ve: ダーザャスリー Sin 3X %3D using (inverse D-operator)

A:

Q: Is this correct?

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.