2 tanh(x) 2) tanh(2x) (H.W) 1+ tanh (x) 2

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: 7. h(x) = tanx- tan 8. h(x) = 3 sec-x

A: we have been given the equations to differentiate w.r.t x

Q: Prove the identity.

A: We will use

Q: tan"x jun's de - | tan"-x dx (n 1) n- 1 tan x sec" r sec x dx (n 1) n- 1

A:

Q: 5). § sech x tanh-x dx

A:

Q: 5. fx3 cos x? dx

A:

Q: 18. [ tan(In x)

A:

Q: 3. lim X-0 sinx sinx-cosx 4. lim x- 5. lim x(cosx-1) sinx-x

A:

Q: sinh (x) esin h-' (x) sin h- (x) Vx²+1 -esin h¯' (x) sin h Vx²–1

A:

Q: entiate g(x)=In(tanhx) in its simplest fo (x)= In(tanhx)sech°x In(tanhx)sech'x tanhx sech'x (x)%D…

A: We have to choose the correct answer from the given option according to the given condition

Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in…

A:

Q: lim x approaches 0 ................ (x^2 - 1)(2 - cos x)

A: To find the limit of the function as x approaches 0, the function is given as follows: x2-12-cos x

Q: 35) y=x.tanh (ans.: x. tanh x(Vx sech' x +2 tanh x))

A:

Q: Limit tant sec 2t 3t

A:

Q: 9. 2x-1 (x+1)(x-2)² -dx

A:

Q: integral tan3(x)sex(x)dx

A:

Q: tan x + i tanh y 1- i tan x tanh y 18. tan z = tan(x + iy)

A: We have to prove

Q: lim cos2x-1/sinx x-> 0

A:

Q: sechx+cshx b) prove that e2x cshx-sechx

A:

Q: 1+tanh² x 1-tanh² x

A: Hyperbolic function

Q: x' sin (tanx*) -1 Integrate 1+x

A: Introduction :

Q: sinh(3-j5) (3 + j4)4 13-j7 (3 – j5)(2-j7)

A: Given sinh(3-j5)3+j443-j52-j73-j7

Q: 1+tanx 2. If f(x) find f'(x) 1-tanx

A:

Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.

Q: f(x)=sinh(x)+2cosh(x)-sech(x) O f(x)=cosh(x)+2sinh(x)-sech(x)tanh(x) O…

A:

Q: limit of x approaching 0 from the right of ((sin(x^2))^x )

A: Given   apply squeeze theorem

Q: tan hx tanh x sec hx-1 sec hx +1

A:

Q: refertoihe Furction (f. thXX f(x)%=X+10 D=DX hox-2xt7 Dox²+3X+n x2+3X+17 Oe-X2-x+3 40-X2-X十9 2.

A:

Q: denivative 12t'de tanx

A:

Q: cIn3 Sn tanh(x) sech³ (x) dx In2

A: This definite integral is based on the Substitution method.  The detailed solution is explained in…

Q: Intergal of (sinh x) / (cosh x + 6) dx

A: To find  Integration of (sinh x) / (cosh x + 6) dx

Q: Area under the curve y = 4 - x2  from x=-3 to x=3

A: Please see the answer bellow.

Q: integral sec^5 x tan x dx

A: we have given that ∫sec5x.tanx.dx

Q: (a) lim tanh(x) (b) lim tanh(x) (c) lim sinh(x)

A: As per our guidelines, we are supposed to answer only the first three subparts. Kindly repost other…

Q: 2. tanh x (12) tanh(2x) = %3D 1+tanh x

A: Answer

Q: sin 2x + 2 arctan (k) lim x→0 In (1+ 3x + sin 2

A: Introduction: So, according to L'Hospital's Rule, if we have an indeterminate form 00 or ∞∞, all we…

Q: | cos³5xsin17xdx

A:

Q: tanx – lim 0 Cos[1 – –

A: Given, -limx→0cos1-tanxx

Q: (sin(x), x 4 x, k(x) = f(x) = -x2 + 4x – 2, х — 6,

A: Consider the given function as fx=sinx     x&lt;0x         0&lt;x&lt;2-x2+4x-2…

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

Q: iv. lim 1- Cos x X->0 v. lim tanx X->0

A: We want to find the limit of the given expression. If we substitute value of the x in expression…

Q: ∫sec^2 x / tan x +1  dx

A:

Q: 1+ tanh x e 2x 1- tanh x

A: Prove the following Use the identities

Q: QI Find f'(x) for 1+ sec-(x) S(x) 1- csc-1(x)

A: