sin' 2x d) lim- x-0 sin' 3x

Q: Evaluate limx-->0 (sin 2x sin 9x)/(x^2) Without using L'Hospital's rule.

A: The given function is limx-->0 (sin 2x sin 9x)/(x^2)Use the expansion for sin x to simplify (sin…

Q: Find the limit. lim sin(9x) 5x

A: We are solving the first question and for the next question post the question again and also mnetion…

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: (1 cosr)dt 1. limx-0 2x -?

A:

Q: Evaluate limx-->2 (sin(x-2))/(x^2+4x-12) Without L'Hospital's rule.

A: limx-->2 (sin(x-2))/(x^2+4x-12)Numerator = sin(x-2)Denominator = x2 + 4x - 12 = x2 +6x - 2x - 12…

Q: 2) Show that sinax _a lim x-0 tanbx b %3D

A: Show that  limx→0sinaxtanbx

Q: find limx->2 X-2 tanQ. Sin O 9) tan a-sin o-tanQ. Sin

A: To find the solution of given equations

Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: tan x B:: Find limx-0

A: Limit of the function

Q: why is limx->0[x^4 * cos(2/3x)] not equal to zero? I thought that if I plug in zero to x^4 it makes…

A: Given that: limx→0x4.cos23x

Q: sin(x – 3) lim X→3 + 6x – 27

A:

Q: 5. Use L'H rule to find (a). lim Inz2 (b). lim (sin x)(In x).

A:

Q: Evaluate: 1- cos(x) 3x2 lim Express your answer in 4 decimal places.

A: According to question,Given limit,limx→0 1- cos x3x2

Q: Evaluate limx-->0 (tan 9x)/(sin 4x) Without using L'Hospital's rule.

A: Obtain the limit without using L’Hospital rule as follows.

Q: 2 lim (cosx)x² =?

A: We have to find the limit

Q: if limxn = x, limyn = y, proof: limxnyn = xy.

A:

Q: Find the limits in Exercis

A: To evaluate: limx→0sin5xsin4x Solution: Given,limx→0sin5xsin4x On simplifying further we get:…

Q: Evaluate limx-->0 (sin^2 2x)/(2x) Without using L'Hospital's rule.

A: The given funtion is (sin^2(2x))/2x for the limit x tends to 0.

Q: If x sinx < 1 2 - 2 cos x hold for all values of x close to zero. Find limx¬0 xsinx ? 2-2cosx

A: 1-x26&lt;xsinx2-2cosx&lt;1 holds for all values of x close to zero. Now, limx→01-x26=1-0=1 &amp;…

Q: lim,-o ([sin x]*) is

A:

Q: Evaluate the limit lim sin (). x-4 lim sin-() = %3D x→4

A: Evaluate the limts

Q: Show that lim sin( does x→0 x2 .not exist

A:

Q: How do you solve question 11 and 12?

A: (11)Given:

Q: se Ľ' Horpitals Rule to find X>0 lim e2x_I SInX

A:

Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

A:

Q: . Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

A: To find the limit of the problem

Q: Find the limit: (а) lim tan 3x x2 sin27x

A:

Q: 1 lim х-0+ \x = 0 Arctan x,

A: Topic = limits  As per guidelines, At a time only one question can be answered.  please repost for…

Q: sin(4x) lim x→0 sin(8x)

A: To find the given limit

Q: Find the limit. lim sin(ax) . x-0 sin(9x)

A: If we plug x=0 in the limit then we get:

Q: lim (In(x))* ?

A:

Q: ve that lim 1 by definition.

A:

Q: Evaluate exactly lim (1 + sinx)²cotx x→0

A: This question is indeterminate form of 1infinity and solved using L Hospital rule.

Q: 6x +55 –5 lim X +5 x+ -5

A:

Q: 2.) lim cot x- sin 2x cotx-1 3.) lim x0 cotx+1

A:

Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: evaluate using Theorem 2 as necessary.

A: We rewrite the given expression as:

Q: is lim (sec x)ot æ 2

A: Apply exponent rule

Q: Use squeeze theorem to shoe that limx-> 2 (x-2)2 (3+sin(x2))= 0

A:

Q: Calculate lim-x+sin x x0 -1+ cos x

A:

Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: alignment at x² + x – 1 limx→ 2x2 — х + 1 has a horizontal at???

A: Topic = Limits

Q: Evaluate using Theorem 2 as necessary.

A: Given: limx→0 x2sin2(x)

Q: 2tan x- x lim, -1 2х -sin " x,

A:

Q: Evaluate limt--&gt;0 (sin 3t)/(sin 6t) WITHOUT using L'Hospital's rule.

A: The given function is limt--&gt;0(sin 3t)/(sin 6t).

Q: lim as x→0 of sin(x4 )/x

A:

Q: sin(3x – 3) lim x² – 1

A:

Q: x-3- – 3VA lim x+0* 0" x- Vx

A: We first try to find the limit  by substitution

Q: Find the value of limx→0 sin(sin x)/x

A: L'Hospital Rule: According to this rule limit of the intermediate form 00  or  ∞∞ can be solved by…

Q: lim as x goes to 0 (sin(2x)+7x2 - 2x / x4 + 2x3 + x2)

A: