solve using L'Hopital's Rule 1. lim      [ 1/(sin^2 x) ]  - [ sinx/x^2 ]    x->0

Q: lim x approaches 0 .............. (sinx)^2

A: Given:              limx→0 sin x2 Plug in the value: x = 0             =sin02

Q: solve using L'Hopitals Rule 6. Lim    (2tanx - sin2x) / x3   x->0

A: limx→02tanx-sin2xx3

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Q: lim x approaches zero, sin4x/sin3x

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Q: Show that  arctan(sinh x) = arcsin(tanh x).

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Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

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Q: sin(51x) lim 16x

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Q: limx->0(sinx/3x)

A: The given expression is,

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A: We need to find slope of tangent line to the given curve.

Q: T-cosx 2. limx-0 3.limx-0 sinx x2 +1 4.limx-0 x+cosx

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: tan(8x) x-0 sin(5x) is indeterminate of type Therefore lim We must use l'Hospital's Rule. The…

A: We are given to find the limit of limx→0 tan(8x)sin(5x); and we have to make use of L hospital rule…

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

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Q: solve using L'Hopital's Rule 4. Lim    [ (sqrt root of 2+x2) / x ] π   x->∞

A: To find: The limit of limx→∞2+x2xπ. Calculation: The limit of limx→∞2+x2xπ apply L'Hospital rule.…

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: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

Q: (sinh x + cosh х)*3 еx

A: Solution:-

Q: lim cos2x-1/sinx x-> 0

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

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Q: x-sinx 1. lim X-0 x-tanx

A: Given function is limx→0x-sinxx-tanx

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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: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

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Q: 2. 2. COS X Sinx lim 4x-X

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A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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A: To find the limit.

Q: Limit as x approaches 0 of Sin(5x)/(2x

A: Limit as x approaches 0 of Sin(5x)/(2x

Q: a) Use suitable sum and difference identities for hyperbolic functions to show that sinh(5x)…

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Q: solve using L'Hopital's Rule 2. Lim      (x-sinx) / (x^3)    x->0

A: To find: The limit of limx→0x-sin xx3. Calculation: Apply L'Hospital rule: limx→0x-sin…

Q: Lim -> 0 Sin3ycot5y/ycot4y

A: limy→0       sin 3y .cot 5yycot4y   =limy→0    sin3y tan4yy tan5y 00farm…

Q: solve using L'Hopitals Rule 5. Lim    (1-cos4x) / xsinx   x->0

A: Given limx→01-cos4xxsinx

Q: solve using L'Hopital's Rule 7. Lim    1/(tan-1)2  -  1/x2    x->0

A: Given the limit as : limx→0 1tan-12-1x2 We need to find the limit by using L' Hopital's Rule. Let's…

Q: lim x→0 (sin3x sin5x/x2) *without use of deritivatives or l'hospital's rule*

A: See the details solution in below

Q: Find f'(x), if f(x)= tan² 4.x. Find f'(x), if f(x) = sin² 2x./cos 2x . Find f"(x), if f (x)= Inx+…

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Q: solve using L'Hopital's Rule 3.  Lim    (ex + e-x  - x2 - 2) / (sin2x - x2)    x->0

A: L'Hopital's Rule: The rule is applicable when the value of the limit function limx→af(x)g(x) is…

Q: Find the value of : sin3x lim x→0 2x

A: This question is based on Limits.

Q: 1- Sinx+ Sin'x 4 X. 2 1-Cosx+Costx 1- Sin'x (1- Sin²x) (x, 1-Cos'x (1-Cosx)

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

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

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Q: 1. lim sin x sin 2x x-0 1-cos x 3x+x+2 . lim X-4x3+8x+1

A: d) To evaluate                       limx→0 sin x sin 2x1- cos x                            =sin (0)…

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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.