Evaluate sin 0 – 1 lim 0 - T/2 In sin 0

Q: 1 lim X→0 SIN²X SINX x2

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: 1 lim (x² –1)sin x+1

A: To find out the limit.

Q: Evaluate: lim 2 tan (r – 2) sin(x – 2)ª

A:

Q: If L = lim x-18 x+ sin(+1) 1 + [x/³ ( and M = lim x→0 of L + M + 11. (172) 1 + 1² sin 2x tan-1 dt…

A: Here we will use L'hospital rule     limx→a fxgx  in 00 or ∞∞ form =limx→a f'xg'x   and Lebnize rule…

Q: 3x²+x d (sin-()+sec='(x) (1) Compute lim cot-1(3x+*+1) (ii) Find- X+00 3x2-7 dx tan-1x+tan-1

A: i).…

Q: 1 o. = 0. Show that lim x² sin -| *

A: Use the property that -1≤siny≤1. Take y=1x, then -1≤sin1x≤1

Q: The value of lim sin x- cos x 1s 2 sin x+3 cosx

A:

Q: (sinx -) tan*(5x) Q3/ 1)- lim, 2)- limx-0 (3sin?x -sinx +1) x sin3 (2x)

A: There are multiple question. As per Bartleby policy Kindly ask other question separately.  Given…

Q: How did limx->π/2 = sin (2x) / x become 0?

A:

Q: lim xS0  .  ...........tan 3x / sin 8x

A: limx→0tan3xsin8x

Q: x cosx-sinx lim x2sinx 1 1/3 3 -1/3 4 -7 2.

A:

Q: lim tanx i. x→ 0 lim In(1+ x)] 11. x→ 0 lim sin ax i1. where a and b are constants. r0sinbxr

A: We are only allow to to do first question and three subpart of question So if you need rest of…

Q: sin 5x lim, X→0

A: Given, limx→ 0sin5xx   Apply the L'Hopital's Rule: limx→ 0sin5xx=limx→ 0cos5x· 51

Q: tan(5x) (1) lim 40 sin(3x) sin(6x) (2) lim x-0 4x3 – 5x

A: 1) limx_0tan(5x)/sin(3x) 2)limx-0sin(6x)/(4x3-5x).

Q: find 49. lim 0 - sin 0 cos e tan 0 - 0 sin 3x - 3x + x² 50. lim sin x sin 2r

A:

Q: Evaluate using Theorem as necessary.

A:

Q: Verify the identity: sin 2x = 2tan x /(1 + tan2 x).

A: Given The identity is sin(2x)=2tan x1+tan2x

Q: 2 3 lim x2.tan=.sin- x) X-00

A:

Q: 1 lim (1 + sin²x)x

A: We have to solve the given limit: limx→01+sin2 x1x This is 1∞ indeterminate form of limit we know…

Q: 43. lim x sin(7/x) 45. lim sin 5x csc 3x

A:

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: Evaluate the limit.

A:

Q: (1) limx¬(1/2)-(tan x)cos x

A: Given that  1)limx→(π2)-(tanx)cosx 2)limx→0x-3(tan-1x-x)

Q: tan 7x i) lim x+0 sin 3x sin(x2 + 3x + 2) j) lim x+2 x + 2

A:

Q: * Find the value of Tx³ + 2. lim [sin (- x3+1] -1 O

A:

Q: tan (3x) lim x→0 sin (2x)

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

Q: In(sin 4x) \ In(sin 8x) lim x → 0

A: We have to evaluate the limitlimx→0ln(sin4x)ln(sin8x)

Q: Find lim n→∞ n + cos(x) Jo ne + sin(x) So -dr.

A:

Q: (b) Write lim > sin n as a definite integral on the interval [0, 7]. Use this definite integral to…

A:

Q: Evaluatelimx→0(sin x - tan x)/x3

A: Evaluate

Q: Evaluate lim sin(a+2x)-2 sin(a+x)+sin a x2

A:

Q: cosxsin2x lim 1-sinx x- 2

A: limx→π2cos x sin2x1- sinx=limx→π2cos x 2 sinx cosx1 - sinx=limx→π22 cos2x  sinx1 - sinx…

Q: 4.x (a) lim 10 sin 5x sin() (b) lim 5x sin 3x (c) lim 10 x2 tan 2.x

A: Read the following instructions once 1. Short method is provided at the end of the subpart (c)…

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

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

Q: Find the discontinuities, if any.  f(x) = sin (x^2 - 2)  f(x) = sec x lim    sin θ / θ2 θ→0+

A:

Q: T+tan x 4. lim sin X→0 tan x-2 sec x,

A:

Q: lim x approches 0 of sin(5x)/7x

A: We have to calculate; A=limx→0sin(5x)7x

Q: Evaluate lim cos(sin 0) O -1 O 1 O does not exist

A:

Q: 1 (*+ stn) (x + sin- lim x→+∞ X.

A: value of the limit is 0.

Q: 1 lim x-0 (sinx ズ→ X.

A: Evaluate the limit limx→01sin x-1x. Rewrite the expression: limx→01sin x-1x=limx→0x-sin xx sin x…

Q: log, (cot-x) 3. lim 1- cosh(2") X -00

A: limit.

Q: et Lim x-0 +e³-x²-2 sin² x-x²

A:

Q: Evaluate lim,→0 ela-cos 7x 8 sin x 7

A:

Q: x sin æ+tan² I lim, 0 1-cos

A: We can solve this as follows:

Q: 1-cos(2x) tan x-sin x Q6- Evaluate: a- limx-0 b- lim x-0 sin (3x) sin³x

A:

Q: lim t→0 of tan4t/sin2t

A:

Q: tan(3z) lim 5z z-0 sin(n)(1-cos(h)) lim h-0 sin(h)(1-cos(h) lim h-0 h3

A:

Q: 7x( cos (4x) – 1) Use l'Hôpital's Rule to evaluate lim sin (5x) – 5x

A:

Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

A:

Q: Evaluate: lim (1+sin 4x)cot ¤ x→0+

A: Topic:- limit calculus

Q: Lim メーvo s'in 5À sin 3X

A: Given: limx→0sin5xsin3x

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

A:

Q: tan*(5x) limx→0 x sin³(2x)

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.