tan 0 cos 20 7. lim 0→0 sin 20 8. lim 0→T/2 tan 0 sin y 1- cosy 9. lim y→0 sin? y 10. lim y→x 1+cosy sin ax 11. lim x csc 3 х 12. lim

Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

A:

Q: If e 2i =sin2 then z = = sin2 = 2 - 2 In(sin2) + 4kT 2i In(sin2) + 4k TI - 2i In(sin2) – 4k T | - 2i…

A: Given that, e-z2i=sin2e-z2i=sin 2e-z2i×ii=sin 2eiz2=sin 2

Q: Differentiation#11

A: We have

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: d) lime tan 0 sin 0 3. e) lim0 sin z-cos z+1 3z

A: We have to find the limits .

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

A:

Q: 1 lim h-0 2h sin(x²)dx = %3D -2h O cos(1) sin(1)

A: Using Fundamental theorem of calculus: ∫-2h0sin(x2)dx=sin(0)-sin((-2h)2)=0-sin(4h2)=-sin(4h2)

Q: 1. y = sin(x) tan(x) 2. y = cos (x) 3. y = cos(tan(x)) 4. y = tan(x) A. y' = -3 cos (x) tan(x) В. у…

A:

Q: 8 sin 3+ 5/ is equal to The number lim | sin(x) dx E. 5. 8 sin(x)dx 8 | sin(x) dx 3. 0 8 8. sin(x)…

A:

Q: = 0 If 2 sin x cos x + V2 cos x = 0. 0, then %3D %3D or

A: 2sin x cos x +2cos x=0

Q: Evaluate S{ [tan (x) – 1]² – sin ()} dx O a. tan (x) – 2 ln|seca|+a cos (플) +C O b. tan (x) + 2 ln…

A: Let I=∫[(tan x-1)2sin xπ]dx        =∫tan2x-2tan x+1-sinxπdx     =∫sec2x-1-2tan x+1-sinxπdx…

Q: 1. sin (5x + ) sin ( x + T /2) %3D 2. tan (3x – T/2 ) = cot 2x 3. COs (x + п /2) sin ( T /2 – 2x )…

A: Given that three trigonometry equation  To find fundamental solution of the question

Q: 7. y = tan³ (2³) (A) 3x² sec(2³) tan(x³) (B)-3x2 sec(³) tan(x³) 8. y = cos(5x) (A) sin(5x) (B)-5…

A: Topic = Derivative As per guidelines, At a time only three sub-parts of a question can be answered.

Q: 0/0 form Evaluate the following limits using l’Hôpital’s Rule.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: 12 If sinh x= find cosh x, tanh x, coth x, sech x, and csch x. 35

A: Given, sinh x = 1235   We have to find  cosh x, tanh x, coth x, sech x  and  csc hx

Q: Evaluate the integrals in Exercises

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 4. y = esec²z (A) sec²rtan resec² z (B)-2 secrtanrx sec²z 5. y= Arccos(x²) 2x (A) √1-2¹ 2x √1-x² (B)…

A:

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: 21 26. lim * Csc 2x o cos Sr 27. lim o tan 2-x + sinx 2x 28. lim ár(cotx)(csc 2x) 30. lim 35, im fan…

A:

Q: Prove the identities sinh (x + y) = sinh x cosh y + cosh x sinh y, cosh (x + y) = cosh x cosh y +…

A:

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

A: Given: z=lnx-y+tanx+y  ……1

Q: 4x[ cos (2x) – 1] sin (5x) – 5x Use L'Hopital's Rule to evaluate lim 4x[ cos (2x) – 1] lim sin (5x)…

A:

Q: O Lim tanx メーンク メ と5 5+s2 2Lim S+1 ン4 3) Lim 3-→ yリアンチアン49 6+ )Lim I+ Cos メ→

A:

Q: 4 points lim h→0 2h cos(x² + 1)dx O 1 O cos(1) O sin(1)

A:

Q: Example 2: find ỹ,y=sin-1 Vx.sec-1 (sin x) Example 1: find ỹ,y=tan-1(x². sin x) Example 3: prove…

A:

Q: (3 tanx-2 cos y)sec" xdx + tanxsin yay = 0

A:

Q: 3 lim z? sin(-

A:

Q: 9. y= sin (r - (z+ 10. y = sin 4 11. y = cos (x – 4. (z + 12. y = coS 13. y = 1+ sin x 14. y = -1+…

A: Matching the graph of functions given by questions 10, 12 and 14

Q: sin 0 – cos 0 lim 0→x/4 tan0 – 1 2(cos x)2 + 3 cos x – 2 lim 2 cos x – 1 y In y – y lim y»e In(y5) –…

A:

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

A:

Q: sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

A: Given system is  sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: 2 sin (4x) lim 2. x2 (1+ cos x)

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

Q: AWO Lim tanx L Szx Lim X-CSc メーラク メ メラ。 OLim ()) S→の 6 Lim di6-X +1XI メー→ロ y4 (3) Lim J→ y2ラッチアy49 4…

A: 1. limx→0tan xx2. limS→∞SS+1S25+S23. limy→∞y4y4-7y3+7y2+9 Note:    Multiple parts are given, we are…

Q: ut. AW O Lim tanx Lim X: CSc Jzx メラ。 メーラク のLim 5→の 6 Lim 16-X + 1x1 メーラマ Sinx 3 Lim 3-→ yテンネマ4 のLm(…

A:

Q: 6 (A) /₁ √== B)/ -x/4 D) dx = tan* (x) sec²(x) dx = C) [rea *² x² ex dx = E) 2x cosh(x²) dx = F) /…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first question. If you…

Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

A:

Q: 7. (3 tan x 1 - 2 cos y) sec² x dx + tan x sin y dy = 0. ANE cos y tan² y ton3 y L

A:

Q: If e/½i =sin2 then z = - 2i In(sin2) + 4k TI 2i In(sin2) + 4k T - 2i In(sin2) – 4kT -2 In(sin2) + 4k…

A: We will find the solution

Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: 1. Solve the DE: tan xsin y y'+(3 tan x-2 cos y) secx= 0

A: Given tanxsinyy'+3tanx-2cosysec2x =0 tanxsinydydx+3tanx-2cosysec2x =0 3tanx-2cosysec2xdx+tanxsinydy…

Q: cos x 13. lim x-(7/2)* 1 – sin x e21 – 1 15. lim - -0 sin t 1 - sin 0 17. lim 0/2 1 + cos 20

A:

Q: find 7. (x, y)→(0,ln 2) In |1 + x² y²| lim et-y 8. lim (x, y)→(1,1) 9. e' sin x 10. (х, у) —-(1/27,…

A:

Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

A:

Q: 9. y"+y= sec² x Ans. y= c, sin x + c2 cos x0 + (sin x ) In(sec x+ tan x)–1

A: Let's find.

Q: Prove the identity.   sinh(x+y) = sinh x cosh y + cosh x sinh y

A: To show that sinhx+y=sinhx coshy+coshx sinhy

Q: 5. y = tan-¹tan x] ab 6. f(x) = x² cos-¹¹-√x²-1 7. f(x) = tan ¹(sin² (2x)) 8. y = (cot ¹(sin¹(x))³

A:

Q: Find 2 sin(x + sin(x + sin a)) – 2 cos(cos 1) lim 2x – T ithout using L'Hôpital's Rule.

A: