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

Q: Investigate lim sin

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Q: Compute lim x-T sinx

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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 limx→π/2(sinx)tanx.

A: We use tan(x)=sin(x)/cos(x)

Q: Find the equation of the tangent line to the function f(x)= x^3-4x at the point where x=0. Do not…

A: Here first we find the slope using the formula m=f'0 Then equation of the tangent at point x = 0,…

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

A: The given limit is,

Q: lim 4x²e sin) sin

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Q: Calculate the limit limx→0+(arcsinx)2x.

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Q: Find the limit. sin(2x) lim

A: To determine the value of the limit.

Q: Find limit   \lim _{x \rightarrow \infty} \sin x/ x

A: A limit refers to the value that a function approaches as the input approaches some value.…

Q: Can the Quotient Law be applied to evaluate lim sin x -? Explain. x+0 X

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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: Compute the derivative ecos(x)arctan(x)

A: The given function ecosxarctanx.

Q: tan(2r) lim 3r+ sin(x)

A: As we know that: limx→afxgx=limx→afxlimx→agx And we know that the identities of limit.…

Q: in your own words, discuss the relationship between the slope of the tangent line, the derivative of…

A: slope of the tangent line, the derivative of a function using the limit process.

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

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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: Find the limits in Exercis

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

Q: how do limits relate to derivatives and integrals? also give examples of when they are used to…

A: Limit of a function is defined as , Let I be an open interval containing x0∈ℝ. Let f : I→ℝ . Then…

Q: Using the fact that lim = 1, show by formal definition of a derivative:

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Q: Find limit sinax lim x→0 sinbx

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Q: Only one of these calculations is correct to evaluate the limit lim (sinhx)*

A: See the details solution in below

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

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Q: - Use the Quotient Rule to find the derivative of the functi

A: We apply quotient rule of derivatives .

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

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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 limits in Exercis

A: Given, limt→0sin1-cos t1-cos t

Q: 3. y = at point (0, -) X-3

A: Topic = Derivative

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

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Q: Evaluate the limit by using the definition of a derivative. log3 (x) – 2 lim x→9 x - 9

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Q: 6. lim (sinx)*

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Q: Find lim In(sin x) cos x by using L' Hospital's rule

A: Let a limit in the form limx→af(x)g(x), where f(a)=g(a)=0, i.e. 00 form, then use L'hopital rule…

Q: 6x +55 –5 lim X +5 x+ -5

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Q: sin 2x lim

A: Consider the given function, limx→∞sin2xx since is a continuous periodic function, as sin2x∈-1,1. as…

Q: Lim (Ln x) L'Haspital Hos

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Q: Find the value of lim tanx

A: As per our guidelines we only solve question number 1 . If you want the solution of other parts…

Q: - lim SinTX メー→ メ ー」

A: We need to evaluate limx→ 1sinπxx-1.

Q: lim x→0 4-Vx+16

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Q: Find lim L(Sn(x – a)). You'll need L'hopital.

A: Using L'hospital rule

Q: Lim (sinx)* -0+

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

Q: Use the fact that sec(x)'= sec(x)tan(x) to find the derivative of arcsec(x).

A:

Q: Calculate lim dt.

A: To evaluate this integral , we will use the fundamental theorem of calculus and Lebnitz theorem.

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: 12) Yex)=

A: The given function f(x)=6x

Q: sin(3x – 3) lim x² – 1

A:

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

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Q: Estimate lim 16 4 is approaching to using a table of functional values.

A: We will use the L. Hopital's rule to find the limit of the given function. to find limx→ 4(16x-4x-4)

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.