lim COS X tanx メー→o <-2メ4リX-8 2lim 3 メ→ 2 xリ_2X メ-2 xツ_2Xメ

Q: 2 cos(4x) – 4x2 – 2 lim - I→0 sin(2x)- x2 - 2x

A: We have to evaluate the limit limx→0 2 cos(4x) - 4x2 - 2sin(2x) - x2 - 2x

Q: х-tanx 2. lim х30 1-со 3 3. lim sinx lnx = 0 x→0+

A:

Q: luaté the lntegr sec2 x Vtan x xp= sec x . tanх + С 2ysec x + C 2/tan x + C

A: We will use substitution method to find the integral of given expression.

Q: P1:

A: Solving

Q: y" + y = sec x tan x

A:

Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: 2+ Cotx 3 3 tanx= 353 3 tanx = Cotx 3 %3D 313 3. 3 3

A: The solution is :

Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

Q: 1) lim y-4 x+6x+5 2) lim 2-3x-4 t+3t2-12t+4 sin3h-2h 3) lim 4) lim 3-4 gin

A:

Q: find dydx 15. y = (sec x + tan x)(sec x - tan x)16. y = x^2 cos x - 2x sin x - 2 cos x17. ƒ(x) = x^3…

A: To Determine: find the derivative  Given: we have y=secx+tanxsecx-tanx Explanation: we have…

Q: 2 tanx + 7tanx+ 5 sec2x 2 tanx + 5 X. %3D

A:

Q: / (6x" – 7Va+ 19x- 8 -- + Evaluate + 14e0* + V11 dx. (You don't have to show the work.)

A:

Q: 5. cot(2x)[2+csc(3x)] 0 x &R 6. tantx - tan2x=-V3(1+tan4xtan2x) xE[-n,"|

A: We have to find the solution in radian

Q: $2tan X sec X

A: See the details solution below

Q: Suppose that 3x² - y² = 1² and y=tsin 0. Find (3). = sin 0 y (1) ¹ (2) and (2) 0 X X

A: Let's find partial derivative of given two equation.

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

A:

Q: 1. y= sin 2x 2. y=2 tan.x 3. y= cot 3x

A: I have provided solutions in step2. because of our guidelines, we can answer only 3 questions so…

Q: (1) y = sinx+1 (2) y = sin 2x (3) y = |cos x (4) y = cosx %3D (5) y = cos x

A:

Q: T-cosx 2. limx-0 3.limx-0 sinx x2 +1 4.limx-0 x+cosx

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: e lim Secx-1 Sinx (-esux) 3}r® २5 ९६० 5x 2 lim ーD6 Sin5x of Sin4x. e lim メーD6 よ + tan 38

A:

Q: Verify the identity.

A: Given: arctanx=12arctan2x1-x2. The interval given is -1&lt;x&lt;1. From the given interval, let…

Q: dx (x² + 1)

A: To solve the given integral

Q: Solve cot x-v3 =0 over [0,2t)

A:

Q: Р5: V4 – 9x²dx (4 — 9х2

A: We have to find the value of ∫4-9x2dx

Q: sin°(,² – 4) (x+2) tan(x+ 2 limy→-2

A: We have to solve

Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: 1. If z=ln (x-y) +tan (x+y) find zxx and zyy

A: Given: z=lnx-y+tanx+y  ……1

Q: x-sinx 1. lim X-0 x-tanx

A: Given function is limx→0x-sinxx-tanx

Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: 2In|tanh(0.5x)| + C 4tan-le0.5x + C E 21n|csc(0.5x) + cot(0.5x)| + C

A:

Q: (1) 1-tank x=sech'x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: 2) y - • sin 0 +2 3元 2元 5元 3元 元 元2

A: The given function,       y=12.sin θ+2

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

A:

Q: P6: x2 x² – 1

A:

Q: 1) y = sin(1 – x²) 2) y = tan 'Vx² + 2x 3) y = tan1 Vt²-1 + csc 1t

A: Given the trigonometric function

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

A:

Q: 4x 3-limx-0 tan5x sin(cos y) 4-lim, y- 2

A:

Q: Use substitution and partial fractions to find the indefinite integral.

A: The given integral is ∫sec2xtan2x+5tanx+6dx. Substitute t=tanx  and dt=sec2x dx in the above…

Q: Lim -> 0 Sin3ycot5y/ycot4y

A: limy→0       sin 3y .cot 5yycot4y   =limy→0    sin3y tan4yy tan5y 00farm…

Q: sin5x(1-2t)dt (6) lim

A: limx→0∫xsin5x1-2tdtx Let  I=∫xsin5x1-2tdt=t-t2xsin5x=sin5x-sin25x-x+x2

Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

A:

Q: sin x cos x -dx (2 sin x – 1)(sin x + 1)

A: To solve: ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Let I = ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Substitute sinx…

Q: (1+ tan(z)) sec² (x) dx

A:

Q: 1)f(x)=sin³ 2x 2)f(x) = 4coshr 3)f(x) )= sinx cos*x 4)f(x) = e*cosx 5)f(x) = 8 Inx %3D

A: image is attached

Q: tanh(x) = 3/5, find the values of the other hyperbolic functions at x.

A:

Q: 3 8. y = sec Зx) 9sec (2 – 3x)tan´(2 – 3x) B. - 9sec (2 - 3x) tan tan (2 3 С. 9 sec' (2 — 3х) tan…

A:

Q: sec² x 12. S 1+tanx

A: here we use       ddxtanx=sec2x see below the calculation and answer s

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step