a sin(ry) dA, where R [0, 2] x (0, ] R

Q: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

Q: Let f(x) = 9 cos(sin(z°)). %3D Then f'(x),

A: Using the chain rule of differentiation,

Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

A:

Q: 2. If f(x, y)=x² cos y-y' sin x-xe'-ye* +2x*y', show that ôxôy ôyôx

A:

Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: Find f(x), where f'(x) = sin(x)+ cos(x) + 1 and f(r) = 2. %3D %3D

A:

Q: d Q 3. Prove that tanx dx sec?x. =

A:

Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

A:

Q: Li sin sin dx = where m n 04: Prove that: %3D where m = n

A: Topic:- integration

Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

A:

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f;(5,5,0).

A:

Q: cos='A F'A where A =atib

A:

Q: 2 = using the relation r= VT show that sin x %3D EX II

A:

Q: Graph the following vector fields

A: (a)known fact:

Q: Using the substitution z = tan 0, evaluate dz, V81 + 4z²

A: The given integration is: ∫181+4x2dx  To evaluate the given integration.

Q: Suppose that f'is continubus, f(o)-o and f(5)= e So f'(x) sin?Cf(x) dx 4) Calculate

A:

Q: Evaluate | f(x) dæ, where -T< x < 0 f(x) = 15 sin(x), 0< æ < n. | f(x) da = -T

A: Solve the following integral

Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

A:

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫√x sin2 (x3/2 - 1) dx, u = x3/2 -…

A:

Q: Using an appropriate substitution, f sin (x)cos (x)dx is equal to:

A:

Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

A: We have to find out

Q: Let - (sin x cos y, COS I sin y, In). Compute div i

A:

Q: (c) Integrate sin"uelog (cosu) . Where n is 482

A: Integrate the sinnuelog(cosu). Where n=482

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Find the egetion of the tanqent line on the interval (o,5) to co.1, 6.2)

A:

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f:(5,5,0).

A: This question is based on Partial derivatives.

Q: on f(z) = e cos x+ ie-Y sin x is entire.

A:

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

A:

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: O sin (z)cos(z)dz

A:

Q: If f(x) = 6 sin z + 6 cos z, then f'(x) = %3D f'(5) =|

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: Evaluate: sin z dz +(°z – z)

A:

Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

A:

Q: Use the indicated substitution to evaluate the integral. 2x cos(x) dx , u = x' sin (x²) + C 2 sin…

A:

Q: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

A:

Q: For f(x) = In(sin(x)), find f'(x)? %3D

A: Given : f(x)=ln(sinx)

Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: Let f(x) = - 8 sin(x)cos(r). df dr d²f dz?

A: Let fx=-8sinxcosx. Then we have to find dfdx, d2fdx2.

Q: /2 cos a sin(sin r) dx

A: using method of substitution

Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

A:

Q: +z/3 + sin z dz

A:

Q: Consider that sin(x) = e, where %3D 0<x< T, then dy tan (x) dx False O TrueO

A:

Q: Find a function f such that ∇f = ex cos yi − ex sin yj + zk.

A: Given, ∇f = ex cos yi − ex sin yj + zk.

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

A: