1- Evaluate: lim (Vx.In(x))? x-0 sin(x') 2- Evaluate: lim x-+0 x tan(x) 3- Evaluate: lim (In z) 4- Evaluate: lim (x" )? X-0

Q: / Find Lim X. tan' 2 X X-100

A:

Q: x-sinx (i) lim x2

A: i) limx->0x-sin xx2

Q: f(x) +3 4+ -4 If lim 3e² 00 0-3 O-4 Oe-3 =e", then lim f(x) =

A:

Q: 2Tan 'x -x 9. lim, 2x – Sin^x

A:

Q: (a) Assume h(a) = f (c)g(a) , f( )=-4, f' () =5, and g(x) = cscx. Find h (x). (b) Find h' using the…

A: (a)

Q: 3x2 + sin(x) lim x(x+ 5)

A: Given rational function is fx=3x2+sinxxx+5

Q: -mestheshien - a) Find the value of the indeterminate form Lim -e Sin x using the L'Hospital's rule.…

A:

Q: 1- cos(x/6) lim II

A: Solve the limit

Q: Example 13: lim x sin(é)

A: To find the limit (x tends to infinity) xsin(2/x)

Q: sin(x²) x→0 In(cosx) 4. Evaluate lim

A:

Q: f(x) If lim f(x) = o and lim g(x) =L < 0, find lim g(x)' XーX0

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Q: QI Find lim tan(x)cos(x)

A: Find out limx→π2-tanxcosx=?

Q: 2) lim-(x-) ta tan x

A:

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: lim 1-e*) X-0 x sin x

A:

Q: sin 20 tan 30 0² (c) Evaluate lim- 0-0

A: Given:        limθ→0sin2θtan3θθ2 Since we have an indeterminate form of type 00, we can apply the…

Q: Use l'Hospital's Rule to evaluate lim X0 sin x-x

A:

Q: lim (-4 0 sin x x

A: Let ,I=limx→ 01sinx-1xTaking cross multilplicationI=limx→ 0x-sinxxsinxI=0-sin(0)0sin(0)I=00Which is…

Q: 1 1 7. lim X-0 (Arctanx)² x2

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: 3* Evaluate (a) lim sin y and (b) lim x→-I /x + 5

A: To evaluate: a) limy→π3 sin y b) limx→-1 3xx+5

Q: sin(4x) g) lim

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Q: e -(1+x)" Evaluate: lim 140 tan x

A: To evaluate: limx→0 e−(1+x)1/xtan⁡x For evaluating the given limit we need to use the expansion of…

Q: エ→2ー Prove that lim sin(1/x) does not exist. Lot II

A:

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: 1 + (a) Lim X-1 'x+1, -2

A:

Q: sin 2x tan xsin 4x 2. Determine lim You may NOT use L'Hospital's x2 sin 3x rule.

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.