sin (x) + cos³(x) = 1 - sin(x) cos(x) sin(x) + cos(x) sin (x) + cos°(x) - (sin(x) + cos(x)) ( sin²(x) – sin(x) + cos(x) sin(x) + cos(x) = sin?(x) – sin(x) cos(x) + = 1- sin(x) cos(x)

Q: L’Hôpital’s Rule is used incorrectly. Describe the error.

A: Given: limx→∞xcos1x

Q: lim (1-cos x1/2) / ln(1+x) ? x-->0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: y = tan(x sin x) O (x + sin x) sec² (x sin x) O (x cos x + sin x) sec² (x sin x) O (x + sin x) sec(x…

A:

Q: 3x+7 sin2x x+x.cosx 1- lim- x2-2 lim 2x2+x 3 - lim- x→0 2 - 00+X x→0 sinx.cosx 1 lim x-1- 1-x2 x-3…

A:

Q: lim 1- cos () X00

A: Given, limx→∞1-cos1x To Find the value of this limit function.

Q: Number 33

A: Given,

Q: lim x → ∞ cos(16/x)^(13.32x^2)

A:

Q: ((주)' lim x (1- cos () COs X->- 00

A:

Q: y=-sec^-2 (In x)

A:

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

A:

Q: 2 sin(-2 x) lim ثم أختر الاجابة ال 0.3) d x-0 4 sin (5 x)

A:

Q: lim x----->0    sin x sin 2x/1- cos x

A: Given:-  limx→0  sinx  sin2x1-cosxTo find:-     value  of the above limit.Concept:-  Use 'L Hospital…

Q: sin 5x + sin 3x 2 cOS X 4 sin x cos 4 sin x cos x 3 X COS -

A:

Q: Lim x-0 e³ +ex -x²-2 sin² x-x²

A:

Q: cos2r – sin2x cos2r For -dr=-F(x)+C_What is F(x)? cosx – sinx 2 sinx + -cosx +cosx+ =sin³x 3 3 O…

A: We know that,  Int(sinx)=cost Int(cosx)=-sinx

Q: Use identities to simplify each expression.

A: cosxsin2x+cos3xsecx=cosxsin2xsecx+cos3xsecx=cos2xsin2x+cos4x…

Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

Q: sin(3 – x) lim с2 — 5х + 6 x→2 x2 – 5x + 6

A:

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 1 3) lim(-- X-0 x VX

A:

Q: sin(cosx * x + Vx) (cosx)2 sin (x²) * cos(x –-) sin(x) – 2

A:

Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

A:

Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

A:

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: cos(-x) 1– sin(-x) 4 x It sin x COS x 4 8 csc x 8 sec x -8 csc x -8 sec x

A: Use trignometric ratio and identities:-

Q: x²+3 1) lim X00 x2+4 1-cos x sin x 2) lim- X-0 sinx 3) lim X-0 ex-1

A:

Q: 8 sin x cos x sec x =

A:

Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

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

Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

A:

Q: V1+ cos x + v1- cos x X =-+-,0<x<. 4 2 an 1+ cos x - V1- cos x - cOS X VI

A:

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

Q: (x² +8) cotx 2 - cos x csc x Find f' (x) when f (x) = 2x cot x – (x² + 8) csc²x A. f' (x) = csc²x 4x…

A: As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Product rule: f·g'=f'·g+f·g' The…

Q: sin2 x cos2 4. sin x- cos4 x X - - 1 4

A: To prove that the left-hand side is equals to the right-hand side.

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 3) lim(-- x0 x V

A:

Q: f(x) = -12sin(x)cos(x) f’(x) = -12cos(2x) f’(π/6) =

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: cos(x (*). cos(x + h) – cos x cos h – 1 sin h - - sin x · h COS x h h

A: Require to verify the identity cosx+h-cosxh=cosxcosh-1h-sinxsinhh

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

A:

Q: sin^2 x + sin x cos x over cos x − 2 cos^3 x

A: This question is based on Trigonometric Formulas to simplify question.

Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: Note: As per company guidelines we solve only first three subparts when multiple parts question…

Q: Lim e^x +e^-x-x²-2/sin²x-x² when x approaches 0

A: The given limit is, This limit is in 0/0 form, so we can apply L’Hospital's rule,

Q: COs x + sinx COS x - Sln x - sin = 2 tan 2x %3D Cos x- sin x COS x + sin x

A:

Q: sin-1(x) – tan-1(x) lim 3x3

A: The given limit involves inverse trigonometric function as well as cubic function and the limit is…

Q: cos 2x 25. cos x- sin x A sinx cos X cos x + sin x 2 cos x + sin x cos x - 2 sinx B 2 sin

A:

Q: lim x->-7  (-x-7)/(4-√(9-x)) lim x->-infinity (√6x^2 - 2x)/(x+8) lim x->0 (7x cos x + sin 5x)/3x

A:

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: 2sin2 x-3sinx+1=0

A: It is a quadratic equation of sin x. So we solve it by factorising.

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: sin-1 x = cos s-'(1 – 2x²) x > 0. |

A: The above problem is solved.

Q: cos(2x)- sin(2x)cos(2x)) cos(x)- sin(x) dx = -F(x) + For C. What is F (x)? 3.

A:

Q: 1-tan x 1+ tan x sec x-CsC X a. sin x + cos x sin x COS X b. sin x +cosX sin x + cos X C. sin x- cos…

A: