71. lim In(x² – 9) X3+

Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

A:

Q: 4. Evaluate lim [In(2+x)-In(1+2.x)] using Calculus 1 limit techniques. Show all steps to justify…

A: To evaluate: limx→∞ln2+x-ln1+2x Solution: We know that, lna-lnb=lnab Therefore,…

Q: lim [r – In(4x + 7)] x→+0

A: To find the limit

Q: Prove that lim, = 1, (x > 0).

A:

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

A:

Q: xCosx-In(1+x)] х-Тапх, limx-ol limx-o[ a) х-Sinx c)

A: a ) given limit is as below:

Q: 21: The final value of :* lim (In(x))?

A:

Q: What is lim In x? x→2

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Q: 5. Use the Squeeze Theorem to evaluate lim sinz 1-00

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: ze" – In(1+#) lim

A: To evaluate the given limit.

Q: 2n +1 a) Using the definition, show that lim n00 3n +4 3

A: Given,           limn→∞2n+13n+4=23

Q: In(x-2) 1- Find , limx→2 In(x² -4)

A: Answer and explanation is given below...

Q: Show limx→∞ xne−x = 0 for all n = 0, 1, 2, . . . . To get started notice that when x ≥ 0, all the…

A:

Q: 10) lim (In x)2/x X00

A: Evaluate the limit in the following way:-

Q: Show that |x2-4|<e ,  when 0<|x-2|<e(5+e)-1 and prove limx->2 x2=4 by using these…

A: Note: The statement is verified by the ϵ-δ statement of limit.

Q: 2. Prove that a. lim, b. lim,1

A:

Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

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Q: Show that 2n lim n+2 = 2,

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Q: lim In x ( - 127/² + 1)

A:

Q: Prove limx→∞(1/x)=0

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Q: Find the limit.

A: We can find the limit of an expression by applying the limit point as value of the variable in the…

Q: 4. Use the e, 8 definition to show that lim,- (4x + 5) = 9.

A:

Q: Prove that lim x 2 = 4. x→ 2

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Q: lim In(x+3) 4) 1

A: Evaluate :     limx→∞ln3xlnx+3

Q: Find the limit.

A:

Q: Show that lim [x2 sin (1/x)] = 0.

A: Given: limx→0x2sin1x

Q: Prove that lim x->0+ √ x [1 + sin2 (2 π/x)] =0

A: Given: limx→0+x1+sin2 2πx By using the property of limit, the limit of a product is the product of a…

Q: 23) lim x In x X-0*

A:

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

A:

Q: tan 2x lim 4.x4

A:

Q: 4. Using the precise definition of a limit, prove lim (2x +8) = 38. x-15

A:

Q: Q. Prove that: Lim tanhx =1 .

A:

Q: Prove that lim5 (x2) = 25

A:

Q: tan3x lim 20 In(1+ x)

A: limx→ 0tan3xln1+xApplying L'Hopital rule=limx→ 0sec23x· 311+xPut x=0=sec23· 0· 311+0=3

Q: lim (In(x))* ?

A:

Q: In(x-2) 1- Find , limx→2 In(x²-4)

A: The given limit is, limx→2ln(x-2)ln(x2-4)

Q: Show that lim (1 – 2²)"dr 0, n 00 0,

A: To show limn→∞∫01(1-x2)ndx=0 without attempting direct intergral.

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

A:

Q: lim (In(x))/x

A: We use L'Hospital rule to evaluate the given limit.

Q: 15. Investigate In (x + 1) In (x + 999) lim lim and In x In x Then use l'Hôpital’s Rule to explain…

A: L' Hopital's Rule is used in the following cases,

Q: 4-If. 2-x s flx) < 2Cos(x) for all x then find: lim (x)

A: Given: 2-x≤f(x)≤2 cos(x)

Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

A:

Q: 44

A: To prove,

Q: 8. Find lim x² In x x→0+

A:

Q: lim (2,1) (0,0) (1 + (x² + y²) In(2² + y²))

A:

Q: Enter a whole or decimal number, or DNE for does not exist or undefined. |0x| lim (5+10=¹). [ - -0+z

A: Topic = Limits

Q: 75. lim [In(1 + x²) – In(1 + x)]

A: Given: limx→∞ln1+x2-ln1+x

Q: evaluate the limit.

A: Given limit is Since Therefore, by applying L'Hopitals' Rule, we have