2 sin x 1 lim is

Q: x(cos(x) – 1), x0 sin(x) – x Evaluate: lim-

A: It is given that,  limx→0xcosx-1sinx-x We have to evaluate it.

Q: 5. x sin 3) lim00 x+1

A: limx→∞x5sin5xx4+1=limx→∞ x5sin5xx41+1x4= limx→∞ x sin5x1+1x4 = limx→∞  sin5x1x1+1x4=limx→∞ 5…

Q: lim ex+7 x-

A: As per the instruction, we will be answering only the first one. For (15),     limx→ -∞…

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

A:

Q: Evaluate

A: Consider the limit Squeeze theorem states that if f(x)<=g(x)<=h(x) for all numbers and at…

Q: 1+sin x lim

A: Given that,  limx→∞ 1+sin xx To evaluate  limx→∞ 1+sin xx=limx→∞ 1x+sin xx=limx→∞ 1x+limx→∞sin xx=0…

Q: Guess the value of lim x 0 sinx/x

A: We try to find the limit by substitution  But 0/0 is indeterminate form.

Q: 2) lim (x – T)tan5

A:

Q: -1 sin (5x) lim

A: The given expression is limx→0sin-15xx the given expression is the indeterminate form 00 Apply L'…

Q: tan x lim x→(T/2)- 2.

A:

Q: æ In(sec(2æ)) (sin(3x))³ lim x→0

A: Given,             limx→0xlnsec2xsin3x3

Q: x sin(3x) lim x→0 sin(x2)

A:

Q: 3* Evaluate (a) lim sin y and (b) lim y x-1 Vx +5

A: we have to evaluate the following: a)  limy→π3 siny b) limx→-13xx+5

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO FO x-5 • lim х-5 х2-25 = 10 FO

A:

Q: - 2 lim c. x→o Sin(x)

A: It is given that X approaching 0 from the left, X<0. Therefore, Sin(x)<0. Therefore, the…

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

A:

Q: 2 cos x tan 7x 2b) find lim

A:

Q:

A:

Q: et sin x — х - lim x → 0 5 cos x – 5 ||

A:

Q: cos(x) sin (2x) lim x X sin(x) – 1

A:

Q: x + sin x 5. lim x 2x + 5

A: We have to solve:      limx→∞x+sin x2x+5

Q: Find lim. Sin (X/y X-T/4

A:

Q: cos x lim

A: the given limit is                   limx→∞cos(x)x as the limit applied directly cannot give the…

Q: (b) lim ln(sin x) x→0+

A: b) limx→0+ln(sin x)

Q: x + sin x 12. lim

A: We will use the properties of limit extensively to find out the limit.

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

A:

Q: tan (3x) lim x→0 sin (2x)

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

Q: lim a sin(1/2),

A: Given,           limx→0xsin1x

Q: Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

A:

Q: x2 – lim x + sin x 2x x→0

A:

Q: x + sin 2x lim x-2 x – sin 2x О з O 2 O 1/3 О 12 O other:

A:

Q: 4x(1 — сos(x)) lim х — sin(x) х>0

A: Because the limit is in 0/0 form. Apply L'hopital's rule.

Q: cos((x) – sin(x) – 1 х) — 1 - 5. lim x→0 2.x

A:

Q: tan nx 3) lim x→0

A:

Q: 2x tan x+ cos I COS T lim

A:

Q: O lim tan(Vx) x² – x x→0+

A:

Q: cos(x) sin (2x) lim x sin(x) – 1

A: To evaluate the limit: limx→π2cos(x)sin(2x)sin(x)-1 Solution: limx→π2cos(x)sin(2x)sin(x)-1 On…

Q: 2Tan 'x - x 9. lim,0 'x0 2x – Sin 'x

A:

Q: -2x – 1 Find lim X+0 sin 3 sin()

A: Using formulae of limits

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

A:

Q: 4 lim sin(x) х>0 х 41

A: Given that

Q: Find lim sin (4 T x). I -3

A:

Q: 2 sin x lim In

A:

Q: Why is it not possible to evaluate by direct substitution?

A: Given: limx→0sin xx To check: Why it not possible to evaluate by direct substitution.

Q: 8 sin((k – 1)x) sin (2x) П ¤(ekz – 1) lim \k=2

A:

Q: tan( xy ) lim (x,y)→(0,1) x´y+x 2 |3|

A: Given function is limx,y→0,1tanxyx2y+x

Q: 4+ sin x d. lim - 1- i cos(x+x) +2 g. lim

A: To find out the limit, substitute 0 for x and find out the limit value

Q: -tan X SinX-CosX Lim

A:

Q: Evaluate lim sin(x)(x +2) 4 8 3x/2+8/2 8 O Does not exist

A:

Q: 10 sin(4x³) 12x8 lim X→0

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.