Prove that (i) Res (tan z, r/2) = - 1

Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

A:

Q: Let F (r, y, z) = sin y i+r cos yj- sin z k.

A: Given,        F(x, y, z)=sinyi+xcosyj-sinzk.

Q: Let /:R'R. S(x. y.2) = (e' tan y,x' In y). Compute D(f).

A:

Q: Prove that J seccu) du - Ln/Sec (u)+ tan (w) + C

A: Integrated in general

Q: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

A:

Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = <cos(z), 16y, -xsin(z)> Hence, F1 = cos(z), F2…

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

A:

Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

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: -Consider the function defined by the base: Find dz ) Prove that дz +y əx дz ду = sin 2z z =…

A: Topic:- application of derivatives

Q: Let F(x, y, z) = z* +x+y sin x +x In z 0, where z =f(x, y), then at (0,0,1) and %3D are equal to:

A: Given,          Fx,y,z=z4+x+ysinx+xlnz=0 , where z=fx,y

Q: Find the value of (f o g)' at x = 1. Tu f(u) = cos u= g(x) = 4/x (fo g)'(1) =

A:

Q: If f(x) = (e19+z) sin(z) 1 20 cos(z) f'(0) then f(0)

A:

Q: 19. Differentiate the following functions. e) f(z) = z? cos 2z + z sin (z?) f) y = In ( sec 2x + tan…

A:

Q: The domain of f(x)= sin(In( is

A:

Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

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: tan? z sec? x + sec a Prove 1-cos I

A:

Q: Consider the function w = f(x,y), where %3D x = r cos 0 and Y = r sin 0 Verify each of the…

A: To find the function in terms of x and y, use the trigonometric identity, cos2x+sin2x=1 and…

Q: (a) Evaluate where c is z = 1 %3D c cos(Tz)

A:

Q: a. Show that If z=x+iy where y >0 Then: 0 < |e*|<1 b. Evaluate cos (i z) – sinh?(z)

A: Using De Moivre's Theorem

Q: Let C be defined by 7(t) = |cos (t), sin (2t), t²| for 0 < t < n 2 sin(Vz) 9x*dx + 2zdy + + 2y ) dz…

A: Using the result that  ∫cF·dr=∫cPdx+Qdy+Rdz=∫P(r→(t))dxdt+Q(r→(t))dydt+R(r→(t))dzdt dt Here,…

Q: Show that U (x, y) = e"cos v,V(x, y) = e"sin v are conjugate harmonic of each other if f = u + iv is…

A: Solution given below

Q: Use a computer algebra system to evaluate (x2 – 2xy) dS. (Round your answer to two decimal places.)…

A: Here we solve the given calculus problem.

Q: 2л where a, b > 0. dx = - ile* + b Prove that %3D

A:

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

A:

Q: Show that F = (2x - 3)i - z j + (cos z)k is not conservative.

A:

Q: Use the convolution theorem to show that cos T sin (t – T) dr 1 sin t. %3D 2

A: Convolution theorem use integration of product of 2 functions and transforms them to pointwise…

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: Find the function r that satisfies the given condition. r'(t) = (5, sin 8t, sec ct); r(0) = (3,3,3)…

A:

Q: Use the Second Fundamental Theorem of Calculus to evaluate cos (E) dx.

A:

Q: H.W. using the relation r = VT show that/(x) = COS X %3D 2

A:

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

A:

Q: z{cos (: -)u(: - )} = a) 3 3

A: We find the given Laplace transform. Formula:  L{cos(at)}=s/(s2+a2)......(1)…

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

A:

Q: Evaluate the integral. 7/2 cos(t) dt V1+ sin?(t)

A:

Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

A:

Q: Prove that [*J₁ [V{x (t−x)}] dx=2 sin }ť.

A:

Q: If f(x) = (e"1+z)' 15 sin(z) +8 cos(z) f'(0) then f(0)

A:

Q: Consider f(t) = (cos t, sin t, t²) and g(x,y,z) = (x² + y² + z², 3x + 4y –- 12z) and h = g(f(t)) =…

A:

Q: Use Fundamental Theorem of Calculus to evaluate the following: d a) sin t dt dx

A:

Q: Find the convolution of f(t)=cos(t)f(t)=cos(t) and g(t)=cos(2t)

A: Given function is f(t)=cos(t) and g(t)=cos(2t)

Q: •T/4 Evaluate 4 sec(0) tan(0)de using the Fundamental Theorem of Calculus, Part 2. TT/4 4 sec(0)…

A:

Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…

A:

Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: (ii) Evaluate the integral. C/4 (sec t tan ti + t cos 2tj + sin? 2t cos 2tk) dt

A:

Q: Use the Second Fundamental Theorem of Calculus to find F'(x). F(x) = 5t cos(t) dt %3D F'(x) =

A: Simple use the second fundamental theorem of calculas   go Through the solution..

Q: (2) Consider the functions f(0) = tan2(0) and g(0) = sec2(0). df (a) Compute de

A: Consider the functions fθ=tan2θ and gθ=sec2θ Here, the objective is to differentiate the function…

Q: Show that the function f(x,y) =x² cos² y+ ysin² x+xe" , satisfies the 2 COS Lipschitz condition in…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.