Solve the following: a. If z = sin(5x + 3y) Find and dx dz ду b. If z=(3x+2y) (4x-5y) Find Oz dz and 8x by c. A cylinder has dimensions r=5 cm, h=12 cm. Find the approximate increase in volume when r increases by 0.2 cm and h decreases by 0.3 cm. d. The radius of a cylinder increases at the rate of 0.2 cm/s while the height decreases at the rate of 0.4 cm/s. Find the rate at which the volume is changing at the instant when r = 8 cm and h = 12 cm. e. If z=sin(x + y); x = u² + v²; y = 2uv Find dz and อน av

Q: ƒ7 In ()dx if sec¹ (3x) dx

A: Integration by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫ddxf(x)·∫g(x) dx dx

Q: Find Sta | tan (ay) dy 32.

A: We have to find integral of given function.

Q: MA 1. Find the following, a. f(5x2 – 6x +3)dx = OWI +2 4t %3D dt

A:

Q: s.fx 5. x3 sin 3x dx

A: We have to find the indefinite integral

Q: 1. L= V1 + 16x6 dx

A: First, we factor out 16 from the radical term, So, it becomes,

Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: dx sinhx

A:

Q: 1 ,-2x dx

A:

Q: Solve For 0LOL27 -sine%3DCOS o 2.

A:

Q: tan (8x) sec³ (8x) dæ 7. 3 ес

A:

Q: | tan? x dx 2

A: Our Aim is to integrate ∫tan2 (x) dx-(i)

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 3) Stan(x) dx

A: The answer provided below has been developed in a clear step by step manner.

Q: 。 x(1-5版) dx

A:

Q: 4. Find / 4 5x² dx. (36x² +20x) 7 ár.

A:

Q: 8. Find sec (30 deg), csc (225 deg),

A:

Q: sec'e -1 3) sin'e

A:

Q: Moa X+la, e dx

A:

Q: 8. (2x° – 3x) dx

A:

Q: C: 2 +xy y?e2 sin x dx

A: The given differential equation is a Bernoulli ODE of the form y'+p(x)y=q(x)yn, whose general…

Q: 3.x + y = 5x5 dy dx

A:

Q: re? e3 1 dx dy dz xyz

A:

Q: 1. Vx dx 3

A:

Q: 1. Solve. X x²-5 +5r+0 - dx

A:

Q: -24 Solve usx dy X. Lu(sinx) dx

A:

Q: 4-x2 C. ye arccos

A: