#24 cal Show that f: IR→IR, x-> (1-x)+cos(1+x³) (a) is continous. ay Show that the map 2 f. IR→IR × →x²ex f: хохе (2 - sinx) is continous.

Q: Differentiate f(w) = sinw + w²tan-1w

A: We have to find differentiation of given function.

Q: FCx): 2x-5xナ3 find f'co).

A: We are solving the first question and for the next question post the question again and also mention…

Q: fyx if f(x, y) = sin(xy) + x² In y cos(xy)- xysin(xy) - cos(xy) + xysin(xy) + cos(xy) – xysin(xy) +…

A:

Q: Find div F and curl F if F(x, y, z) = 2eyi- 7 cos y j + 4 sin² z k. div F= curl F=

A:

Q: Q1/: a: Using the relation showthat J-va (x) = 2 cos x

A: We have to solve given problem:

Q: 3.1 (x+1) (x'+5x+2) ふeren ta ee

A: Topic = Derivative As per guidelines , At a time only one question can be answered.

Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

A:

Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

A:

Q: Let f(z) = 4 cos I-3 tan z. %3D S(2) =D %3D

A:

Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

A:

Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

A:

Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

A:

Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

A:

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: ) FIND F'6): c. f() - x 2- 3x2 F. f6) = VI-x

A: f(x)=x2-3x2differentiate w.r.t.…

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

A:

Q: Write the function f(x,y) = xcosh(x)cos(y) - ysinh(x)sin(y) + i(xsinh(x)sin(y) + ycosh(x)sin(y)) in…

A: f(z)=Re(z)cosh(Re(z))cos(Im(z))−Im(z)sinh(Re(z))sin(Im(z))+i(Re(z)sinh(Re(z))sin(Im(z))+Im(z)cosh(Re…

Q: TT 4 3. f(1 + sinx) dx + f(1 + sinx) dx 0 TU 4

A:

Q: 3 prove that sinh (2) isine

A: Since you have posted multiple questions, we will provide the  solution   only to the first question…

Q: For the function 1-cos.x 1-cosy + -=C, where C is a real constant, which of the following is equal…

A:

Q: Evaluate this function of z = cos x sin y; x = u – v, y= u² + v². Use chain - dz rule to find ди А.…

A: The given function are z=cosx siny; x=u-v, y=u2+v2.   Rewrite the given the function as follows.…

Q: 3 x° In x x° with respect to X - Find the derivative of y a) 6x - a2 b) None of these c) p6 ln x x2…

A: Given query is to find the derivative of the expression.

Q: Vリ What is F'(;) 4 ? 16 π 4 π ミ|N

A:

Q: x+y %3D 21. Prove that tan-x + tan-'y tan - xy.

A: Using tan(A+B) =( tan(A) + tan(B) )/(1- tan(A) tan(B) ).

Q: Six)ax = [glu) du 1f flx): 3x-1 Solw) au ? Consider what is sec (3*) ·

A: we have to integrate