Use L’Hopital’s rule to show that limx→π/2 2 tan x/sec2 x = 0

Q: 5 tan(4x) x→0 3 sin(2x) Evaluate lim using L’Hôpital's rule.

A: The  L'Hopital's rule is: Suppose, f(x) and g(x) are two functions and their limit is given as:…

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: why is the limit as x approaches 0 equal to 1/5 in the equation: ((sinx)/(5x))

A: The given limit is,

Q: x* +x + 2x+2 lim x-1 x+1

A:

Q: How many times must l'hôpital's rule be applied to evaluate ex - e-X – 2x lim X + 0 X- sinx

A:

Q: Rearrange lim x* so that we can apply L'hopital's rule. *→0+

A: Follow the steps.

Q: By using Sandwich Theorem, prove that lim sin x x-0 r

A: We have to prove that limx→0sin xx = 1 using sandwich theorem. Sandwich theorem states that- Suppose…

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

A: Show that  limx→0sinaxtanbx

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

A: We need to find the limits of the given expressions by using the L.Hopital rule. For (1),

Q: Find the limit of * sin(6x) limx→0 sin(2x)

A: Given problem is :

Q: sin xy lim 0.

A:

Q: Evaluate the limit sin 9x lim x →0 sin 3x

A: We can solve the problems by finding the value of the function at  the given limit.

Q: Use the Squeeze Theorem to evaluate lim sin(tan x) sech(secx).

A: It is required to calculate the limit limx→π2-sintanxsechsecx. The squeeze theorem states that "Let…

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

A:

Q: Use the Squeeze Theorem to evaluate lim sin(tan r) sech(secr). ес

A:

Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) csch x 8118

A:

Q: 4. Use L'Hopital's rule to evaluate lim(1 – 2 sinh(r))ach(=).

A: 4) To evaluate: limx→0(1-2sinh(x))csch(x)  which is in 1∞ form.

Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

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: Find the limits in Exercise

A: Given, limθ→0cosπθsinθ we know expansion of sinx sinx=x-x33!+x55!-.... now put this expansion in…

Q: Evaluate limx-->0 (x^2)/(sin^2(7x)) Without using L'Hospital's rule.

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: Find limit sinax lim x→0 sinbx

A:

Q: Find the limit. lim sin(5x) 6x

A: Given: limx→0sin5x6x

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

A:

Q: Show that limx→0(√x) cos(1/2x) = 0.Show your work.

A:

Q: se L'Hopitals's rule to find lim xIn(e* – 1).

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

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

A:

Q: Use l'Hopital's rule to find the limit. 20 lim x sin

A:

Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

A:

Q: 3. Use Squeeze Theorem to evaluate lim 1-0+ sin(In r) In(sin æ)"

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: Find the value of the limit: lim x→0* sinx+ tan x

A: Given query is to find the value of the indicated limit

Q: Use l’Hôpital’s rule to find the limits

A: To evaluate the given limits lim x→0sin3x-3x+x2sinxsin2x Solution: Since we know that, lim…

Q: Evaluate limt-->0(tan 4t)/(t sec t) Without using L'Hospital's rule.

A: To calculate the required limit without using the indeterminate form

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: Show that lim x sin l/x = 0.                   x→ 0

A: It is known that the absolute value of sine function is not greater than 1, then  -x≤xsin1x≤x

Q: lim x→0 for sin(4x)/3x

A:

Q: Evaluate lim wing sin2x +7x²-2x Wir 'Hopi L'Hopital's rule,

A: Consider the given expression. limx→0sin2x+7x2−2xx2x+12 Simplify the denominator.…

Q: Compute limx→0 sin(x) − x divided by  x^3

A: We have to evaluate the limit: limx→0sinx-xx3 After putting limit value we can see that this is 00…

Q: find the following limits if exist:- limx-0 1-cosx x sinx

A:

Q: Compute limx→0 sin(x) − x / x^3

A: To find the limit, simplify the expression and then apply the limit to each term in the expression.…

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

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

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: B) Without using L'Hopital's rule, find: lim 3-Vx2+9 x2

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.