21) lim x-4/In x X-0+

Q: Prove that lim +1) = 3 using the e--definition.

A:

Q: lim x*

A:

Q: 1 1. lim In (x- 2) x-3 X-3+

A:

Q: Suppose lim, =1. Prove that lim -(-1)* = %3D

A: Given: limn→∞ an=1To prove: limn→∞ 1n ∑k=1n -1k a2k=0

Q: Clearly show why evaluating lim x (In x)2 requires repeated application of L'Hopital's rule. Show…

A: We have to evaluate the limit of the function fx=xlnx2 using the L' Hopital's rule. To find the…

Q: Prove the limit statement using epsilon-delta 3x2 - 8x-3 x -3 2) lim x-3 = 10

A:

Q: 2. Evaluate the limit: TC 1000 lim x-7- (x-7)2 lim x→8+ (8 - x)3

A: the given limit is: limx→7-πx-72-limx→8+10008-x3 we have to evaluate the given limit.

Q: 8. lim x - 4 + In (x – 4)

A:

Q: 2 Compute limx→16; 1-x2 1 X-1

A:

Q: Calculate lim x->∞ x-In x .

A: Given expression We need to find the limit.

Q: Use L'Hopital's Rule to evaluate the exact value of lim(x² – 2x+1)*-1.

A:

Q: 3) lim-) 1 х-1 \x-1 In x)

A:

Q: 5. lim X-0 e2x-1

A:

Q: lim (-In x) : 1|

A: Property of limit: limx→akfx=klimx→afx Calculation: The limit can be obtain by using the above…

Q: 6. lim In(2+x)-In(1+x) 5. lim In(1+x*)-In(1+x)]

A: Topic = Limits

Q: 22- iz lim 23 +1 10 -1 0 20 00

A:

Q: Prove that lim š +1) = 3 using the e-8-definition.

A:

Q: 4. Use L'Hopital's Rule to find (a). lim 22-In 2 3+2z

A:

Q: 9. Compute lim x tan (). x→0

A:

Q: х —9 Determine lim V6 - Vx-3 x→9 |

A: HERE WEMUST KNOW ABOUT L'HOPITAL RULE

Q: 17. If lim- X- 200 – 4n + kn² then k =

A: Given

Q: Compute lim 1+-

A:

Q: х2—1 lim х-1+ In(x)

A:

Q: ,2 30. lim x In x

A: Topic = Limits

Q: 5. Use L'Hopital's rule to evaluate e* +2 limy-o ex +

A: limx→∞ex+2xex+5x

Q: Find f(a)  a=2

A: We know that the definition of derivative is: We write the given equation in this format and find…

Q: (In x)² lim

A:

Q: 12-x-x 1- Prove that lim -7 %3D x-3 V6+x-3

A: our objective is to find the limit

Q: 37. lim (In 2x – In(x + 1)) X00

A:

Q: Show that lim -e-* = 0

A:

Q: In(1-x)+ x Evaluate lim using L'Hopital's rule. x-0 x?

A:

Q: 5. Calculate limit: lim x³+2x²-x-2 x-2 x3+x2-2x

A:

Q: 25. - lim (tan x)*om

A:

Q: Prove that 2 +22- -6 lim 3, tan x-3tan x lim cos(x+7/6) V2* - 2-

A:

Q: -Show that lim xsin

A:

Q: lim (In(3x + 1) – In(2x + 1))

A: To evaluate the below limit

Q: Prove that lim -- (x + 1)

A: we have to prove that: limx→-1-5x+13=-∞   L.H.S:…

Q: 2 In x lim x→+∞

A:

Q: 5. lim In(1+x)-In(1+ x)] 6. lim In(2+x)-In(1+x)]

A: limx→∞ ln1+x2-ln1+x

Q: Compute lim tan x→3+ -1 х2-9

A:

Q: Find the limit.  lim x--> infinity  ln (3x2-1/x2+1)

A:

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: 11. lim [In(1 + x²) – In(1 + x)]

A:

Q: 8. Find lim x² In x x→0+

A:

Q: 1 lim In csch (1– 2x,

A: Let L is the value of given Limit

Q: Evaluate

A: Given: The limit expression as limx→∞lnxx To find: The value of given expression.

Q: Determine the limit (In(12 - 1 x - 1 x² + 12 x³)-In(25 – 1 x - 4 x2 + 25 x³)) lim X- 00

A:

Q: 75. lim [In(1 + x²) – In(1 + x)]

A: Given: limx→∞ln1+x2-ln1+x